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

Why are you not divide 600 by 96000, which is exactly divisible?

Please tell me.

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

LCM = 600.

600)9999(16
-------------
600
3999
3600
399 --> reminder.

9999 - 399 = 9600 answer.

@Pravin.

I agree with you. Thank you.

399 is subtracted so that the number may be exactly divided.

To understand this, take an example.

If we divide 20 by 3, the remainder is 2. So 20 is not divisible by 3 but if I subtract remainder from it i.e. 20 - 2 = 18, now it will be exactly divisible by 3. (ie) 18/3 = 6.

Hope this helps!

Why we should take LCM of number instead of taking HCF? Anyone can explain clearly?

Guys, In question, they ask 15, 25, 40 & 75 is divisible by the greatest number of four digits.
So they give 4 digits means.

9999 is the big digit, okey leave this one .

Given options a)9000 b) 9400 c)9600 d)9800.


First we take L.C.M of 15, 25, 40 & 75 = 600.

In options first big one is 9800 so divide with 600 (9800/600=is not divisible).
So take second big one is 9600 so divide with 600(9600/600=is divisible with 16).
Third big one is 9400 so divide with 600(9400/600 = is not divisible).
Fourth big one is 9000 so divide with 600(9000/600 = is divisible with 15).

Then what's the question is the biggest 4 digit number is divisible with 15,25,40&75.
Here given options two 4 digit's number is divisible (i.e.9000, 9600).

In question ask the greatest 4 digit number (9000 & 9600 which is big one) And obviously answer is 9600.

If you do 'daa' method to get the LCM for 15, 25, 40, 75 as 5, 5, 3, 8. Then to multiply 5 * 5 * 3 * 8 = 600.

5 | 15, 25, 40, 75
|___________________
5 | 3, 5, 8, 15
|___________________
3 | 3, 1, 8, 3
|_____________________
8 | 1, 1, 8, 1
|_______________________
===> 1, 1, 1, 1


Therefore, 5 * 5 * 3 *8 = 600.

Greatest 4 digit number = 9999.
LCM = 15, 25, 40, 75.

15 = 5 * 3.
20 = 5 * 5.
40 = 5 * 2 * 2 * 2.
75 = 5 * 5 * 3.

Then the lcm is => 5 * 5 * 2 * 2 * 2 * 3 = 600.
So, divide greatest number by 600.
9999/600 = 399.
Required number = (9999 - 399) = 9600.

So option "c".

Thanks @Sruthi.

Better take lcm of all numbers i.e. 600 and tye greatest 4 digit number that will be divisible by 600 will be the answer.

In this case, 9000 and 9600 are divisible by 600 and 9600 is the greater one.

Simple as possible.