Find the smallest square number that is divisible by each of the numbers 8, 15 and 20

We know that the number that is perfectly divisible by each of the numbers 8, 15, and 20 is their LCM.

Therefore,

LCM of 8, 15, and 20 is:

2 × 2 × 2 × 3 × 5 =120

Here, prime factors 2, 3, and 5 do not have their respective pairs.

Therefore, 120 is not a perfect square

Therefore, 120 should be multiplied by 2 × 3 × 5, i.e. 30, to obtain a perfect square

Hence,

The required square number = 120 × 2 × 3 × 5

= 3600