Question

Find the smallest square number which is divisible by each of the numbers 6, 9, and 15.

Answer 1

The least number divisible by each one of 6, 9, and 15 is their LCM.

The LCM of 6, 9 and 15 is 2 × 3 × 3 × 5 = 90.

Prime factorisation of 90 is 90 = 2 × 3 × 3 × 5.

The prime factors 2 and 5 are not in pairs. Therefore 90 is not a perfect square.

In order to get a perfect square, each factor of 90 must be paired. So we need to

make pairs of 2 and 5. Therefore, 90 should be multiplied by 2 × 5, i.e., 10.

Hence, the required square number is 90 × 10 = 900.