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.

Why do we take LCM of the given numbers, but not HCF?

How you get 399?

We can also take 9800 as a base then we have to divide 9800 by 600 which gives 200 remainder and we subtract 200 from 9800 will give the answer 9600.

How to devide 9999 by 600? please explain.

How that remainder come 399 please tell me?

9999 divide 600 which give only remainder for 133 but there they are said 399 how its?

What if we take 6 digits?

Hi all,

Another method to answer this question is just break all four (15, 25, 40, 75) in to prime numbers.

15 = 5*3.
25 = 5*5.
40 = 8 (2*2*2) *5.
75 = 5*3*5.

Now here we can see the common divisors are 5, 3 and 8.

So the number which is divisible by 5, 3 and 8 is the right answer which is option C 9600.

How remainder 399 comes, by my calculation remainder must be 133? Please show the remainder calculation.