# 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 1 of 12.
Shashank Ravoor said:
1 year 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.

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.

(81)

Vignesh said:
3 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.

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.

(29)

Luci said:
3 years ago

How to guess when to LCM find and when to HCF find out?

(25)

Imtiyaz said:
2 years 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.

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.

(8)

Divya said:
4 years ago

Why we are using lcm here instead of hcf?

(7)

G.Shangugapriya said:
4 years ago

Can anyone explain, Why don't we use HCF for this sum?

(7)

Rattan said:
3 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.

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.

(7)

Lale Di Jaan said:
2 years ago

Here, We can also multiply 600 by the quotient.

i.e. 600*16 = 9600.

i.e. 600*16 = 9600.

(7)

Rahul said:
5 years ago

As question given greatest number then how we do LCM method ? Greatest number means HCF nah?

(3)

Prathyusha said:
5 years ago

How to identify whether the question given is based on LCM or HCF?

(2)

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