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

Calculating without LCM method

Shortcut way to get 600

In the option A) is given 9000 and B) 9400 and C) 9600 and D) 9800

To subtract from highest number first i.e (D-C) 9800-9600= 200 and (B-A) 9400-9000= 400

Now (D-C)=200
(B-A)=400

Add 200 + 400= 600

The questions says greatest four digit that means in every first digit is 9..so therefore there will be 4 greatest digits of 9 i.e is 9999

Hence 9999-600= 9,399
(Therefore the first digit is 9 so the rest 3 digit is 399 and hence 9999 - 399)

9999-399= 9600

We need to find highest 4 digit least common multiplier. So lcm of given numbers is 600. It's a three digit number but need to find 4 digit number. 600*8=4800 but I still need to be in range below 10000. 4800*2=9600.

How to find 600 is LCM?

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.

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

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.

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

How do we know whether to find lcm or hcf?

Why do we use LCM instead of HCM?

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.