# Problems On HCF And LCM

## 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