Question

how to find the least four digit number which when divided by 15,20 and 30 leaves no remainder

Answer 1

Hi!

Here is the answer to your question.

The given numbers are 15, 20 and 30.

Prime factorization of 15 = 3 × 5

Prime factorization of 20 = 2 × 2 × 5

Prime factorization of 30 = 2 × 3 × 5

LCM of 15, 20 and 30 = 2 × 2 × 3 × 5 = 60

Least four digit number which when divided by 15, 20 and 30 leaves no remainder is the multiple of LCM of 15, 20, 30 i.e., 60.

Now, 60 × 16 = 960 and 60 × 17 = 1020

∴1020 is the least four digit number which when divided by 15, 20 and 30 leaves no remainder.

Cheers!