Question

Find the smallest number of 5 digits which is exactly divisible by 15, 24 and 40 .

I am unable to understand the following solution . kindly help.

LCM of 15,24 and 40 is 120.

I divide 10000 by 120 , quotient is 83 and remainder is 40.I require to subtract 40 from 120 and add the difference to 10000 in order to get the required number .Why donI need to subtract ?

Answer 1

When you substract 40 from 120,remainder becomes zero(because remainder is 40),now add 80 to compensate that substraction.

Another simple method is given below

We have remainder=40

You have to substract 40 from 10000 ,then we will get a 4 digit number which is divisible by 120
10000-40=9960

But we need a five digit number. So the next number which can be divided by 120 or which is a multiple of 1200 is 9960+120 = 10080