We know that,

The smallest number that is divisible by each o0f these numbers is their L.C.M

So,

L.C.M of 8, 12, 15, 20 = 120

Resolving into prime factors, we get

120 = 2 × 2 × 2 × 3 × 5

So, for making it a perfect square we have to multiply it by 2 × 3 × 5 = 30

Multiplying the number by 30, we get

Required number = 120 × 30

= 3600