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

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### Exercise :: Problems on H.C.F and L.C.M - General Questions

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

Explanation:

Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)

= H.C.F. of 48, 92 and 140 = 4.

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

Explanation:

Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322.

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

Explanation:

L.C.M. of 2, 4, 6, 8, 10, 12 is 120.

So, the bells will toll together after every 120 seconds(2 minutes).

 In 30 minutes, they will toll together 30 + 1 = 16 times. 2

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

Explanation:

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

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

Explanation:

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399. Required number (9999 - 399) = 9600.