# 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 2 of 12.

G.Shangugapriya said:   4 years ago
Can anyone explain, Why don't we use HCF for this sum?
(7)

Divya said:   4 years ago
Why we are using lcm here instead of hcf?
(7)

Pratik Sakharkar said:   4 years ago
Hello.

They told that greatest 4 digits no right.

So to calculate the common multiple take lcm of 15,25,40,75.

The answer will come 600 right.

Now to check the biggest 4 digits no divide the lcm by 9000, 9400, 9600, 9800.
9000/600= 15.
9400/600=47/3 i.e 15.66 not valid.
9600/600=16.
9800/600=49/3 i.e 16.33 not valid.

So the proper 4 digits greater no is 9600 which is divided by lcm which is not in fraction, so the answer is 9600.
(1)

Djay said:   4 years ago
75*8=600 lcm.

And find option divisible by 600.

Prathyusha said:   5 years ago
How to identify whether the question given is based on LCM or HCF?
(2)

Rahul said:   5 years ago
As question given greatest number then how we do LCM method ? Greatest number means HCF nah?
(3)

Yash said:   5 years ago
When greatest FOUR Digit number is to be found it means the number won't exceed 9999 so when we take 600 modulus 9999 we get remainder 399 which means that we are having 399 left after dividing 9999 with 6000 so we subtract 399 from 9999 so that remainder becomes zero and we get the greatest 4 digit number.

As the LCM of four number is 600 the number divisible by them are multiple of 600 i.e.

600
1200
1800
2400
3000
3600
4200
4800
5400
6000
6600
7200
7800
8400
9000
9600 -----> this is the greatest 4 digit number divisible.
10200.

Rithika said:   5 years ago
I can't understand this problem clearly please anyone help me.

Yogeshwari said:   5 years ago
Please anyone explain how will come lcm 600 from the 4 digits.

I didn't understand. Please help me.

Geetinder said:   5 years ago
Lcm =600,
Then 600*14= 8400,
But I need a range between 9000 to10000,
Then 600*15=9000,
But 600*16= 9600,
600*17=10200 but I want the biggest number below 10000
So 9600 is the right answer.

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