Aptitude - Problems on H.C.F and L.C.M - Discussion

The Logic here is this:

We have to find the greatest 4 digit number which is divisible by 15, 25, 40 and 75, hence it is a multiple of all these.

The LCM(15, 25, 40, 75) = 600 i.e. the least common multiple.

Hence all other common multiples of 15, 25, 40 and 75 will be multiples of 600 as well.

So to find the highest 4 digit one among all the common multiples, divide all the options by 600 to check which is perfectly divisible by 600. We get 9600, which is the answer.

Please tell why we have to take lcm instead instead of hcf and in which situation I have to take lcm or hcf?

5) 15,25,40,75
------------
5) 3,5,8,15
------------
3) 3,1,8,3
------------
1,1,8,1

Now,

LCM = 5*5*3*8 = 600.

Why do we use LCM instead of HCM?

How do we know whether to find lcm or hcf?

When greatest FOUR Digit number is to be found it means the number wont 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 no. divisible
10200

L.C.M. of 15, 25, 40 and 75 is 600.

Now, We find out the multiples of 600 of lowest/smallest five digit number i.e.600*17=10200.

Therefore, Greatest four digit number divisible by 15, 25, 40 and 75 can easily found by 600*16 i.e 9600.

This is simplest & easiest method.

I don't know how to do LCM & HCF, anyone can you help me how to do?

LCM of 15: 5 X 3.

25: 5^2.

40: 5 X 2^3.

75: 5^2 X 3.

From each highest power of 5 = 5^2, 2 = 2^3, 3 = 3.

So 5^2 X 2^3 X 3 = 600.

How to find 600 is LCM?