# Problems on H.C.F and L.C.M

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

A. 120
B. 240
C. 360
D. 480

2 | 24 – 36 – 40
——————–
2 | 12 – 18 – 20
——————–
2 | 6 – 9 – 10
——————-
3 | 3 – 9 – 5
——————-
| 1 – 3 – 5

L.C.M. = 2 x 2 x 2 x 3 x 3 x 5 = 360.

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

L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 – 37) = 23.  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

L.C.M. of 5, 6, 7, 8 = 840.
So, the required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
So, Required number = (840 x 2 + 3) = 1683.

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

Correct Answer: D. 46 minutes and 12 seconds