Question

10. Find the least number of five-digits which when divided by 12, 15, 18 and 27 leaves remainder 3 in each case

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Answer 1

Take LCM of 12, 15 and 18.

Factors are

12=2*2*3,

15=3*5,

18=2*3*3.

Their LCM=2*2*3*3*5

=180.

Because smallest 5 digits number is 10000.

Let us divide it by 180

then for a quotient 55 remainder is 100

if we add 80 to it then it will be completely divided by 180 with a quotient 56.

Therefore 180*56=10080

So smallest 5 digits number divisible by 12, 15, and 18

is 10080

Answer 2

He did it correct but forgot to add the remainder
So final answer is 10083