# 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:

119 comments Page 1 of 12.
Shashank Ravoor said:
2 years 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.

(128)

Luci said:
3 years ago

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

(36)

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.

(33)

Rattan said:
4 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.

(10)

Imtiyaz said:
3 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.

(10)

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.

(9)

G.Shangugapriya said:
4 years ago

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

(8)

Divya said:
5 years ago

Why we are using lcm here instead of hcf?

(7)

Zero said:
7 months ago

LCM = 600.

See the option,

Great number = option D = not multiple of 600.

Again see 2nd greatest = option se C = which is multiple of 600.

So, option C is the correct answer.

See the option,

Great number = option D = not multiple of 600.

Again see 2nd greatest = option se C = which is multiple of 600.

So, option C is the correct answer.

(6)

Suresh said:
2 months ago

When understanding the question it's clearly saying the highest 4-digit number can be divisible by 15, 25, 40 and 75.

Now see the options the Highest number is 9800. Try to divide it by 15. 9800 not divisible by 15. So 9800 is not the correct option.

Again check 9600. It can be divisible by 15, 25, 40, 75. So, 9600 is the greatest of all remaining so the answer is 9600.

Now see the options the Highest number is 9800. Try to divide it by 15. 9800 not divisible by 15. So 9800 is not the correct option.

Again check 9600. It can be divisible by 15, 25, 40, 75. So, 9600 is the greatest of all remaining so the answer is 9600.

(6)

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