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
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 1 of 12.

Ram said:   1 decade ago
How to find the l.c.m number the value is 600?

Thom said:   1 decade ago
How to find 600 is LCM?

Nitya said:   1 decade ago
Just find the lcm of 15, 40, 25, 75.

Then you will get the answer as 600.

Darshana said:   1 decade ago
How to find the l.c.m number the value is 600?

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.

Pavan said:   1 decade ago
Why subtracted 9999-399?

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.

Aparna said:   1 decade ago
@vishnu.

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

It is divisible by 40.

Gwene said:   1 decade ago
Why only 9999? among those 4 numbers 9800 is greater so why not 9800?

Gwene said:   1 decade ago
Vishnu why should we divide by 40?


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