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

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 5)
5.
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
9000
9400
9600
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.

Discussion:
118 comments Page 1 of 12.

How to find the l.c.m number the value is 600?

How to find 600 is LCM?

Just find the lcm of 15, 40, 25, 75.

Then you will get the answer as 600.

How to find the l.c.m number the value is 600?

To find the LCM use prime factorization:
15: 5 x 3
25: 5 x 5
40: 5 x 8 = 5 x 2 x 2 x 2
75: 15 x 5 = 5 x 5 x 3
LCM: Every prime factor such that none are repeated:
5 x 3 (from 15) x 5 (from 25) x 2 x 2 x 2 (from 40) and since two 5s and 3 are already there you dont take anything from 75.
so LCM is 5 x 3 x 5 x 2 x 2 x 2 = 600

Then just find the greatest 4 digit number divisible by 600. Which is shown and explained well by the problem explanation.

Why subtracted 9999-399?

Just check if the answers are divisible by 40(one of the numbers given)...It's easy to notice that 9000,9400 and 9800 will not be divisible. So, it's obviously 9600.

@vishnu.

How 9000, 9400 and 9800 are not divsible by 40?.

It is divisible by 40.