# 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:
116 comments Page 1 of 12.

Shashank Ravoor said:   2 days ago
@All.

Here's my explanation:

The given numbers are 15,25,40 and 75 are multiples of 5. So I can associate these numbers with respect to 5. The greatest numbers that are given in the options should be added as the sum of digits and check whether it's completely divisible by 5.
Now going through options:

A: 9+0+0+0=9 -> not divisible by 5
B: 9+4+0+0=13 -> same as A
C: 9+6+0+0=15 -> completely divisible by 5.

Hence, Option C is the answer.
(1)

Lale Di Jaan said:   10 months ago
Here, We can also multiply 600 by the quotient.
i.e. 600*16 = 9600.
(2)

Imtiyaz said:   1 year ago
The four-digit largest no.is 9999.
And we the LCM of 15,25,40,75 which is 600,
Divide 9999 by 600 you will get 16.665 And Multiply only 16 of 600 you will get 9600.
(4)

Luci said:   2 years ago
How to guess when to LCM find and when to HCF find out?
(3)

Vignesh said:   2 years ago
15,25,40,75 .

It's all div by 5 right so,

In option we have 9000,9400,9600,9800 .. Sum of the digits = div by 5 ..
In 9+0+0+0 =9, 9+4+0+0=13, 9+6+0+0=15 its divided by 5. So the answer was 9600.
(15)

Rattan said:   2 years ago
15 = 3*5
25 = 5*5
40 = 8*5
75 = 3*5*5
Clearly, HCF of these numbers will be 3*5*5*8.
So a number to be divisible by all four a no. must be divisible by 3, 5, and 8.

The only numbers in the options given that are divisible by these 3 are 9000 and 9600, but the question asked for the greatest no. Which means the answer is 9600.
(1)

Angelina said:   2 years ago
How did we get 9999? Explain it.

Shivni said:   3 years ago
@ Tejas Kumblar

Nice explanation. Thanks.

G.Shangugapriya said:   3 years ago
Can anyone explain, Why don't we use HCF for this sum?
(2)

Divya said:   3 years ago
Why we are using lcm here instead of hcf?
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