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Problems On L.c.m And H.c.f MCQs

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1

Find the least square number which is divisible by 10, 12, 15 and 18?

Option A: 1600

Option B: 900

Option C: 3600

Option D: 2500

Correct Answer: 900 ✔


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2

Three men start together to travel the same way around a circular track of 11 kilometers in circumference. Their speeds are 4, 5 and 8 kilometers per hour respectively. When will they meet at a starting point?

Option A: 11 hours

Option B: 12 hours

Option C: 220 hours

Option D: 22 hours

Correct Answer: 11 hours ✔


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3

Find the least multiple of 13 which when divided by 6, 8 and 12 leaves 5, 7 and 11 as remainders respectively? A. 143 B. 169 C. 260 D. 221

Option A: 143

Option B: 169

Option C: 260

Option D: 221

Correct Answer: 143 ✔


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4

Find the least number which when divided by 6, 7, 8, 9 and 10 leaves 1, 2, 3, 4 and 5 as remainders respectively, but when divided by 19 leaves no remainder?

Option A: 5073

Option B: 5016

Option C: 5054

Option D: 5035

Correct Answer: 5035 ✔


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5

Find the least number which when divide by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders respectively, but when divided by 7 leaves no remainder?

Option A: 210

Option B: 119

Option C: 126

Option D: 154

Correct Answer: 119 ✔


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6

A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?

Option A: 7203

Option B: 2403

Option C: 3603

Option D: 4803

Correct Answer: 7203 ✔


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7

Find the greatest number of four digits which when divided by 10, 15, 21 and 28 leaves 4, 9, 15 and 22 as remainders respectively?

Option A: 9654

Option B: 9666

Option C: 9664

Option D: 9864

Correct Answer: 9654 ✔


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8

Find the least number which when divided by 35 leaves remainder 25, when divided by 25 leaves remainder 15 and when divided by 15 leaves remainder 5?

Option A: 420

Option B: 515

Option C: 435

Option D: 518

Correct Answer: 515 ✔


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9

What is the least number which when divided by 8, 12, 18 and 24 leaves the remainders 4, 8, 14 and 20 respectively?

Option A: 78

Option B: 68

Option C: 58

Option D: None

Correct Answer: 68 ✔


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10

The wheels revolve round a common horizontal axis. They make 15, 20 and 48 revolutions in a minute respectively. Starting with a certain point on the circumference down wards. After what interval of time will they come together in the same position?

Option A: 1 min

Option B: 2 min

Option C: 3 min

Option D: None

Correct Answer: 1 min ✔


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11

Two numbers 4242 and 2903 when divided by a certain number of three digits, leave the same remainder. Find the number?

Option A: 101

Option B: 103

Option C: 107

Option D: 113

Correct Answer: 103 ✔


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12

There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number?

Option A: 5

Option B: 7

Option C: 11

Option D: 13

Correct Answer: 5 ✔


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13

There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?

Option A: 17

Option B: 29

Option C: 23

Option D: 31

Correct Answer: 29 ✔


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14

How many minimum number’s of whole square slabs are required for paving the floor 12.96 meters long and 3.84 meters side?

Option A: 216

Option B: 192

Option C: 108

Option D: 256

Correct Answer: 216 ✔


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15

A room is 4 meters 37 cm long and 3 meters 23cm broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose?

Option A: 485

Option B: 431

Option C: 391

Option D: 381

Correct Answer: 391 ✔


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16

Find the size of the largest square slabs which can be paved on the floor of a room 5 meters 44 cm long and 3 meters 74 cm broad?

Option A: 56

Option B: 42

Option C: 38

Option D: 34

Correct Answer: 34 ✔


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17

A wholesale tea dealer 408 kilograms, 468 kilograms and 516 kilograms of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box?

Option A: 50

Option B: 36

Option C: 24

Option D: 12

Correct Answer: 12 ✔


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18

A merchant has three different types of milk: 435 liters, 493 liters and 551 liters. Find the least number of casks of equal size required to store all the milk without mixing.

Option A: 51

Option B: 61

Option C: 47

Option D: 45

Correct Answer: 51 ✔


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19

Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same?

Option A: 53

Option B: 112

Option C: 108

Option D: 106

Correct Answer: 106 ✔


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20

Find the greatest number which will divide 25, 73 and 97 as so to leave the same remainder in each case?

Option A: 12

Option B: 18

Option C: 24

Option D: 32

Correct Answer: 24 ✔


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21

An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent?

Option A: 3

Option B: 4

Option C: 5

Option D: 6

Correct Answer: 3 ✔


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22

A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work?

Option A: 39

Option B: 40

Option C: 37

Option D: 35

Correct Answer: 37 ✔


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23

In finding the HCF of two numbers, the last divisor was 41 and the successive quotients, starting from the first, where 2, 4 and 2. The numbers are______?

Option A: 700,400

Option B: 820,360

Option C: 800,500

Option D: 820,369

Correct Answer: 820,369 ✔


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24

Least perfect square number, exactly divisible by 21, 36 and 56 is_________?

Option A: 3600

Option B: 504

Option C: 441

Option D: 7056

Correct Answer: 7056 ✔


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25

HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is_______?

Option A: 36

Option B: 66

Option C: 132

Option D: 264

Correct Answer: 132 ✔


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26

Five bells first begin to toll together and then at intervals of 5, 10, 15, 20 and 25 seconds respectively. After what interval of time will they toll again together?

Option A: 5 min

Option B: 5.5 min

Option C: 5.2 min

Option D: None

Correct Answer: 5 min ✔


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27

Find the least number of five digits which is exactly divisible by 12, 15 and 18?

Option A: 1080

Option B: 10080

Option C: 10025

Option D: 11080

Correct Answer: 10080 ✔


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28

The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is________?

Option A: 1994

Option B: 1494

Option C: 1349

Option D: 1496

Correct Answer: 1349 ✔


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29

A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is_______?

Option A: 31

Option B: 41

Option C: 51

Option D: 61

Correct Answer: 31 ✔


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30

The smallest number when increased by ” 1 ” is exactly divisible by 12, 18, 24, 32 and 40 is__________?

Option A: 1439

Option B: 1440

Option C: 1459

Option D: 1449

Correct Answer: 1439 ✔


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31

The least number of five digits that have 144 their HCF is__________?

Option A: 10085

Option B: 10080

Option C: 10075

Option D: 10070

Correct Answer: 10080 ✔


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32

The greatest number of four digits that have 144 for their HCF is__________?

Option A: 9930

Option B: 9903

Option C: 9935

Option D: 9936

Correct Answer: 9936 ✔


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33

The least number of four digits which is divisible by 4, 6, 8 and 10 is_________?

Option A: 1080

Option B: 1085

Option C: 1075

Option D: 1095

Correct Answer: 1080 ✔


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34

The greatest number of five digits which is divisible by 32, 36, 40, 42 and 48 is_________?

Option A: 90730

Option B: 90725

Option C: 90715

Option D: 90720

Correct Answer: 90720 ✔


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35

The product of two digits number is 2160 and their HCF is 12. The numbers are________?

Option A: (36,60)

Option B: (12,180)

Option C: (96,25)

Option D: (72,30)

Correct Answer: (36,60) ✔


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36

Four bells begin to toll together respectively at the intervals of 8, 10, 12 and 16 seconds. After how many seconds will they toll together again?

Option A: 246 seconds

Option B: 242 seconds

Option C: 240 seconds

Option D: 243 seconds

Correct Answer: 240 seconds ✔


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37

The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is________?

Option A: 1267

Option B: 1265

Option C: 1261

Option D: 68

Correct Answer: 1267 ✔


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38

The least number which when add 3 to it, completely divided 8, 12 and 18 is_______?

Option A: 71

Option B: 70

Option C: 69

Option D: 68

Correct Answer: 69 ✔


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39

The least number which when divided by 8, 12 and 16, leave in each remainder 3, is_______?

Option A: 71

Option B: 70

Option C: 69

Option D: 51

Correct Answer: 51 ✔


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40

The least square number which divides 8, 12 and 18 is________?

Option A: 100

Option B: 121

Option C: 64

Option D: 144

Correct Answer: 144 ✔


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41

The least number which when divided by 16, 18 and 21, leave the remainder 3, 5 and 8 respectively is__________?

Option A: 982

Option B: 893

Option C: 1024

Option D: 995

Correct Answer: 995 ✔


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42

The product of two numbers is 2025 and their HCF is 15 their LCM is__________?

Option A: 2040

Option B: 2010

Option C: 135

Option D: 150

Correct Answer: 135 ✔


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43

Find the H.C.F of 54/9, 3 9/17 and 36/51?

Option A: 17/6

Option B: 6/153

Option C: 6

Option D: 17

Correct Answer: 6/153 ✔


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44

Find the H.C.F of 204, 1190 and 1445?

Option A: 34

Option B: 17

Option C: 85

Option D: 204

Correct Answer: 17 ✔


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45

Find the H.C.F of 12, 16, 18 and 24?

Option A: 1

Option B: 2

Option C: 3

Option D: 4

Correct Answer: 2 ✔


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46

HCF of 3/16, 5/12, 7/8 is__________?

Option A: 2/47

Option B: 3/47

Option C: 1/48

Option D: 5/48

Correct Answer: 1/48 ✔


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47

LCM of 1/3, 5/6, 5/4, 10/7 is_________?

Option A: 10/7

Option B: 10

Option C: 10/11

Option D: 11/10

Correct Answer: 10 ✔


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48

LCM of 455, 117, 338 is________?

Option A: 10670

Option B: 106470

Option C: 104670

Option D: 107470

Correct Answer: 106470 ✔


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49

LCM of 87 and 145 is_______?

Option A: 1305

Option B: 435

Option C: 875

Option D: 48

Correct Answer: 435 ✔


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50

LCM of 18 and 27 is_________?

Option A: 85

Option B: 89

Option C: 54

Option D: 91

Correct Answer: 54 ✔


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51

LCM of two numbers is 138. But their (Greatest common divisor) GCD is 23. The numbers are in a ratio 1:6. Which is the largest number amongst the two?

Option A: 46

Option B: 138

Option C: 69

Option D: 23

Correct Answer: 138 ✔


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52

Greatest Common Divisor of two numbers is 8 while their Least Common Multiple is 144. Find the other number if one number is 16.

Option A: 108

Option B: 96

Option C: 72

Option D: 36

Correct Answer: 72 ✔


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53

The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is_________?

Option A: 28

Option B: 32

Option C: 40

Option D: 64

Correct Answer: 40 ✔


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54

Which of the following has the most number of divisors?

Option A: 99

Option B: 101

Option C: 176

Option D: 182

Correct Answer: 176 ✔


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55

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is_________?

Option A: 123

Option B: 127

Option C: 235

Option D: 305

Correct Answer: 127 ✔


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56

A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?

Option A: 26 min 18 sec

Option B: 42 min 36 sec

Option C: 45 min

Option D: 46 min 12 sec

Correct Answer: 46 min 12 sec ✔


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57

The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:

Option A: 3

Option B: 13

Option C: 23

Option D: 33

Correct Answer: 3 ✔


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58

The least number of four digits which is divisible by 15, 25, 40 and 75 is_________?

Option A: 9000

Option B: 9400

Option C: 9600

Option D: 9800

Correct Answer: 9600 ✔


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59

The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is_________?

Option A: 30/7

Option B: 30/98

Option C: 60/147

Option D: 50/294

Correct Answer: 30/7 ✔


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60

What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?

Option A: 196

Option B: 630

Option C: 1260

Option D: 2520

Correct Answer: 630 ✔


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61

Which of the following fractions is the largest?

Option A: 7/8

Option B: 13/16

Option C: 31/40

Option D: 63/80

Correct Answer: 7/8 ✔


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62

The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is__________?

Option A: 276

Option B: 299

Option C: 322

Option D: 345

Correct Answer: 322 ✔


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63

The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?

Option A: 24

Option B: 48

Option C: 56

Option D: 60

Correct Answer: 60 ✔


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64

Product of two co-prime numbers is 117. Their L.C.M should be__________?

Option A: 1

Option B: 117

Option C: equal to their H.C.F

Option D: Cannot be calculated

Correct Answer: 1 ✔


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65

If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to__________?

Option A: 55/601

Option B: 601/55

Option C: 11/120

Option D: 120/11

Correct Answer: 11/120 ✔


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66

The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is__________?

Option A: 10

Option B: 46

Option C: 70

Option D: 90

Correct Answer: 10 ✔


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67

The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is__________?

Option A: 279

Option B: 283

Option C: 308

Option D: 318

Correct Answer: 308 ✔


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68

The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is__________?

Option A: 12

Option B: 48

Option C: 84

Option D: 108

Correct Answer: 84 ✔


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69

Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:

Option A: 40

Option B: 80

Option C: 120

Option D: 200

Correct Answer: 40 ✔


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70

The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is__________?

Option A: 28

Option B: 32

Option C: 40

Option D: 64

Correct Answer: 40 ✔


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71

Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is________?

Option A: 75

Option B: 81

Option C: 85

Option D: 89

Correct Answer: 85 ✔


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72

The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is__________?

Option A: 1

Option B: 2

Option C: 3

Option D: 4

Correct Answer: 2 ✔


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73

The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is_________?

Option A: 101

Option B: 107

Option C: 111

Option D: 185

Correct Answer: 111 ✔


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74

The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is__________?

Option A: 4

Option B: 6

Option C: 8

Option D: 12

Correct Answer: 4 ✔


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75

The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is__________?

Option A: 12

Option B: 16

Option C: 24

Option D: 48

Correct Answer: 48 ✔


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76

Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are__________?

Option A: 4, 8, 12

Option B: 5, 10, 15

Option C: 10, 20, 30

Option D: 12, 24, 36

Correct Answer: 12, 24, 36 ✔


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77

H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 * 35 * 52 * 72. The third number is__________?

Option A: 22 * 35 * 72

Option B: 22 * 53 * 72

Option C: 25 * 52 * 72

Option D: 23 * 35 * 72

Correct Answer: A. 22 * 35 * 72 ✔


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78

The G.C.D of 1.08, 0.36 and 0.9 is________?

Option A: 0.03

Option B: 0.9

Option C: 0.18

Option D: 0.108

Correct Answer: 0.18 ✔


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79

Find the lowest common multiple of 24, 36 and 40.

Option A: 120

Option B: 240

Option C: 360

Option D: 480

Correct Answer: 360 ✔


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80

Find the highest common factor of 36 and 84.

Option A: 4

Option B: 6

Option C: 12

Option D: 18

Correct Answer: 12 ✔


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81

H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is__________?

Option A: 180

Option B: 360

Option C: 540

Option D: 1260

Correct Answer: 180 ✔


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82

1095/1168 when expressed in simplest form is:

Option A: 13/16

Option B: 15/16

Option C: 17/26

Option D: 25/26

Correct Answer: 15/16 ✔


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83

Which of the following has most number of divisors?

Option A: 99

Option B: 101

Option C: 176

Option D: 182

Correct Answer: 176 ✔


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84

252 can be expressed as a product of primes as__________?

Option A: 2 * 2 * 3 * 3 * 7

Option B: 2 * 2 * 2 * 3 * 7

Option C: 3 * 3 * 3 * 3 * 7

Option D: 2 * 3 * 3 * 3 * 7

Correct Answer: 2 * 2 * 3 * 3 * 7 ✔


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85

A drink vendor has 80 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn’t want to mix any two drinks in a can. What is the least number of cans required?

Option A: 35

Option B: 37

Option C: 42

Option D: 30

Correct Answer: 37 ✔


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86

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?

Option A: 110

Option B: 124

Option C: 96

Option D: 117

Correct Answer: 117 ✔


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87

Find the greatest number that, while dividing 47, 215 and 365, gives the same remainder in each case?

Option A: 3

Option B: 4

Option C: 5

Option D: 6

Correct Answer: 5 ✔


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88

Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case?

Option A: 16

Option B: 17

Option C: 18

Option D: 19

Correct Answer: 16 ✔


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89

Find the greatest number that exactly divides 35, 91 and 840?

Option A: 5

Option B: 6

Option C: 7

Option D: 8

Correct Answer: 7 ✔


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90

Find the lowest 4-digit number which when divided by 3, 4 or 5 leaves a remainder of 2 in each case?

Option A: 1020

Option B: 1026

Option C: 1030

Option D: 1022

Correct Answer: 1022 ✔


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91

Find the greatest 4-digit number exactly divisible by 3, 4 and 5?

Option A: 9985

Option B: 9960

Option C: 9957

Option D: 9975

Correct Answer: 9960 ✔


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92

Find the smallest number which when increased by 5, divisible by 6, 9, 15, 20 and 24?

Option A: 344

Option B: 355

Option C: 366

Option D: 377

Correct Answer: 355 ✔


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93

A gardener was asked a plant flowers in a row containing equal number of plants. He tried to plant 6, 8, 10 and 12 in each row, but 5 plants left in each case. When he planted 13 in a row, no plant was left. Find the number of plants with him?

Option A: 245

Option B: 125

Option C: 485

Option D: 845

Correct Answer: 845 ✔


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