## Problems On HCF And LCM

1. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

A. 4

B. 7

C. 9

D. 13

Answer: Option A

2. 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:

A. 276

B. 299

C. 322

D. 345

Answer: Option C

3. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

A. 4

B. 10

C. 15

D. 16

Answer: Option D

4. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

A. 4

B. 5

C. 6

D. 8

Answer: Option A

5. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000

B. 9400

C. 9600

D. 9800

Answer: Option C

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

A. 101

B. 107

C. 111

D. 185

Answer: Option C

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

A. 40

B. 80

C. 120

D. 200

Answer: Option A

8. The G.C.D. of 1.08, 0.36 and 0.9 is:

A. 0.03

B. 0.9

C. 0.18

D. 0.108

Answer: Option C

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

A. 1

B. 2

C. 3

D. 4

Answer: Option B

10. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

A. 74

B. 94

C. 184

D. 364

Answer: Option D

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

A. 120

B. 240

C. 360

D. 480

Answer: Option C

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

A. 3

B. 13

C. 23

D. 33

Answer: Option C

14. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

A. 1677

B. 1683

C. 2523

D. 3363

Answer: Option B

15. 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 again at the starting point ?

A. 26 minutes and 18 seconds

B. 42 minutes and 36 seconds

C. 45 minutes

D. 46 minutes and 12 seconds

Answer: Option D

16. 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:

A. 279

B. 283

C. 308

D. 318

Answer: Option C

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

A. 196

B. 630

C. 1260

D. 2520

Answer: Option B

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

A. 12

B. 16

C. 24

D. 48

Answer: Option D

19. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

A. 1008

B. 1015

C. 1022

D. 1032

Answer: Option B

20. 252 can be expressed as a product of primes as:

A. 2 × 2 × 3 × 3 × 7

B. 2 × 2 × 2 × 3 × 7

C. 3 × 3 × 3 × 3 × 7

D. 2 × 3 × 3 × 3 × 7

Answer: Option A