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problems on l c m and h c f MCQs

Practise focused problems on l c m and h c f questions with marked answers for exam preparation and subject revision.

problems on l c m and h c f Mcqs
1. Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same?
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A. 106

B. 112

C. 108

D. 53

2. Find the highest common factor of 36 and 84.
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A. 6

B. 12

C. 18

D. 4

3. The least number which when add 3 to it, completely divided 8, 12 and 18 is_______?
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A. 71

B. 69

C. 68

D. 70

4. Find the least square number which is divisible by 10, 12, 15 and 18?
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A. 900

B. 1600

C. 3600

D. 2500

5. Least perfect square number, exactly divisible by 21, 36 and 56 is_________?
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A. 7056

B. 504

C. 3600

D. 441

6. 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___________?
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A. 345

B. 276

C. 299

D. 322
7. The least number which when divided by 8, 12 and 16, leave in each remainder 3, is_______?
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A. 51

B. 71

C. 70

D. 69

8. 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?
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A. 5054

B. 5035

C. 5073

D. 5016

9. LCM of 18 and 27 is_________?
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A. 91

B. 54

C. 89

D. 85

10. 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?
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A. 45 min

B. 26 min 18 sec

C. 42 min 36 sec

D. 46 min 12 sec
11. 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?
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A. 240 seconds

B. 246 seconds

C. 242 seconds

D. 243 seconds

12. The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is________?
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A. 1267

B. 1265

C. 1261

D. 68

13. 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?
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A. 485

B. 391

C. 381

D. 431

14. 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?
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A. 12 hours

B. 22 hours

C. 220 hours

D. 11 hours
15. The least square number which divides 8, 12 and 18 is________?
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A. 144

B. 121

C. 64

D. 100

16. Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are__________?
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A. 12, 24, 36

B. 5, 10, 15

C. 10, 20, 30

D. 4, 8, 12

17. Find the greatest number that exactly divides 35, 91 and 840?
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A. 6

B. 8

C. 7

D. 5

18. 252 can be expressed as a product of primes as_______________?
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A. 2 * 3 * 3 * 3 * 7

B. 3 * 3 * 3 * 3 * 7

C. 2 * 2 * 2 * 3 * 7

D. 2 * 2 * 3 * 3 * 7
19. 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?
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A. 435

B. 515

C. 420

D. 518

20. The smallest number when increased by 1 is exactly divisible by 12, 18, 24, 32 and 40 is__________?
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A. 1449

B. 1440

C. 1439

D. 1459

21. The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is_________?
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A. 30/7

B. 30/98

C. 50/294

D. 60/147

22. Find the H.C.F of 54/9, 3 9/17 and 36/51?
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A. 6/153

B. 17

C. 6

D. 17/6

23. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
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A. 23

B. 3

C. 13

D. 33

24. Which of the following has the most number of divisors?
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A. 176

B. 182

C. 99

D. 101

25. H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is___________?
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A. 180

B. 1260

C. 360

D. 540

26. Find the H.C.F of 12, 16, 18 and 24?
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A. 3

B. 4

C. 2

D. 1

27. 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______?
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A. 820,360

B. 820,369

C. 700,400

D. 800,500

28. How many minimum numbers of whole square slabs are required for paving the floor 12.96 meters long and 3.84 meters side?
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A. 108

B. 192

C. 256

D. 216
29. Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:
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A. 80

B. 120

C. 200

D. 40
30. Which of the following has most number of divisors?
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A. 99

B. 101

C. 182

D. 176
31. Find the greatest 4-digit number exactly divisible by 3, 4 and 5?
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A. 9957

B. 9985

C. 9960

D. 9975

32. 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.
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A. 61

B. 45

C. 51

D. 47

33. What is the least number which when divided by 8, 12, 18 and 24 leaves the remainders 4, 8, 14 and 20 respectively?
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A. None

B. 58

C. 78

D. 68
34. Find the greatest number which will divide 25, 73 and 97 as so to leave the same remainder in each case?
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A. 12

B. 32

C. 18

D. 24
35. Find the greatest number that, while dividing 47, 215 and 365, gives the same remainder in each case?
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A. 6

B. 5

C. 4

D. 3

36. The least number of five digits that have 144 their HCF is__________?
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A. 10085

B. 10070

C. 10080

D. 10075

37. Find the lowest common multiple of 24, 36 and 40.
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A. 360

B. 120

C. 480

D. 240

38. 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__________?
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A. 70

B. 90

C. 46

D. 10
39. 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?
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A. 17

B. 31

C. 23

D. 29
40. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is_________?
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A. 64

B. 40

C. 28

D. 32

41. 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?
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A. 154

B. 210

C. 126

D. 119
42. The product of two digits number is 2160 and their HCF is 12. The numbers are________?
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A. (72,30)

B. -12,180

C. (96,25)

D. (36,60)
43. Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case?
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A. 17

B. 19

C. 18

D. 16
44. Find the smallest number which when increased by 5, divisible by 6, 9, 15, 20 and 24?
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A. 355

B. 366

C. 377

D. 344

45. The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is__________?
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A. 3

B. 4

C. 1

D. 2
46. 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___________?
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A. 11/120

B. 601/55

C. 120/11

D. 55/601

47. The greatest number of four digits that have 144 for their HCF is___________?
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A. 9930

B. 9903

C. 9936

D. 9935

48. 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?
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A. 39

B. 40

C. 35

D. 37
49. Which of the following fractions is the largest?
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A. 13/16

B. 7/8

C. 63/80

D. 31/40

50. LCM of 1/3, 5/6, 5/4, 10/7 is_________?
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A. 7-Oct

B. 10

C. 11-Oct

D. 10-Nov