# 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:

Answer: Option

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 12 of 12.
Aparna said:
1 decade ago

@vishnu.

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

It is divisible by 40.

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

It is divisible by 40.

Vishnu said:
1 decade ago

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.

Pavan said:
1 decade ago

Why subtracted 9999-399?

Rahul said:
1 decade ago

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.

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.

Darshana said:
1 decade ago

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

Nitya said:
1 decade ago

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

Then you will get the answer as 600.

Then you will get the answer as 600.

Thom said:
1 decade ago

How to find 600 is LCM?

Ram said:
1 decade ago

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

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