# LCM and HCF Questions and Answers

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All questions relevant to LCM and HCF are collected from previous year question papers form Bank, IBPS, SSC, PSC, CGL, RBI, CAT, MAT and other competitive exam.

## Model Questions on LCM and HCF

1. The H.C.F. and L.C.M. of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is

A. 48

B. 36

C. 24

D. 16

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

A. 24

B. 48

C. 56

D. 60

3. The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is

A. 1120

B. 4214

C. 5200

D. 5600

4. The greatest number by which 2300 and 3500 are divided leaving the remainders of 32 and 56 respectively, is

A. 136

B. 168

C. 42

D. 84

5. The ninth term of the sequence 0, 3, 8, 15, 24, 35, …… is

A. 63

B. 70

C. 80

D. 99

6. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be:

A. 5

B. 25

C. 45

D. 225

7. A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be

A. 1

B. 2

C. 7

D. 17

8. Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.

A. 183

B. 243

C. 443

D. 123

9. Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is

A. 21

B. 24

C. 23

D. 84

10. The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is

A. 4023

B. 4032

C. 4302

D. 4203

## Sample Papers to Practice

11. The sixth term of the sequence 2, 6, 11, 17, ……….. is

A. 24

B. 30

C. 32

D. 36

12. The smallest number, which when divided by 5, 10, 12 and 15, leaves remainder 2 in each case; but when divided by 7 leaves no remainder, is

A. 189

B. 182

C. 175

D. 91

13. A number, when divided by 136, leaves remainder 36. If the same number is divided by 17, the remainder will be

A. 9

B. 7

C. 3

D. 2

14. The sum of two numbers is 84 and their HCF is 12. Total number of such pairs of number is

A. 2

B. 3

C. 4

D. 5

15. A 4 digit number is formed by repeating a 2 digit number such as 1515, 3737, etc. Any number of this form is exactly divisible by

A. 7

B. 9

C. 3

D. 2

16. The HCF and LCM of two numbers are 13 and 455 respectively. If one of the number lies between 75 and 125, then, that number is:

A. 78

B. 91

C. 104

D. 117

17. The H.C.F. and L.C.M. of two numbers are 12 and 336 respectively. If one of the numbers is 84, the other is

A. 36

B. 43

C. 72

D. 96

18. The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is

A. 2/35

B. 3/25

C. 4/35

D. 2/25

19. If ‘n’ be any natural number, then by which largest number ({ n }^{ 3 } – n) is always divisible?

A. 3

B. 6

C. 12

D. 18

## Download Practice Exercise

20. The LCM of three different numbers is 120. Which of the following cannot be their H.C.F?

A. 8

B. 12

C. 24

D. 35

21. A number when divided by 49 leaves 32 as remainder. This number when divided by 7 will have the remainder as

A. 4

B. 3

C. 3

D. 5

22. The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. It they all change simultaneously at 10:15:00 AM, then at what time will they again change simultaneously?

A. 10: 16:54 AM

B. 10:18:36 AM

C. 10:17:02AM

D. 10:22:12AM

23. The least number, which is to be added to the greatest number of 4 digits so that the sum may be divisible by 345, is

A. 50

B. 6

C. 60

D. 5

24. L.C.M. of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers?

A. 140

B. 80

C. 60

D. 20

25. When ‘n‘ is divisible by 5 the remainder is 2. What is the remainder when { n }^{ 2} is divided by 5?

A. 2

B. 3

C. 1

D. 4

26. Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time they meet at the starting point for the first time?

A. 1800 seconds

B. 3600 seconds

C. 2400 seconds

D. 4800 seconds

27. The greatest number that can divide 140, 176, 264 leaving remainders of 4, 6, and 9 respectively is

A. 85

B. 34

C. 17

D. 2

28. There are 4 terms in an AP. such that the sum of two means is 1 10 and product of their extremes is 2125. The 3rd term is

A. 65

B. 75

C. 55

D. 45

29. The LCM of two numbers is 864 and their HCF is 144. If one of the number is 288, the other number is :

A. 576

B. 1296

C. 432

D. 144

30. There are 24 peaches, 36 apricots and 60 bananas and they have to be arranged in several rows in such a way that every row contains the same number of fruits of only one type. What is the minimum number of rows required for this to happen?

A. 12

B. 9

C. 10

D. 6