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But on Factorising 120 we find that it's factors are not in pairs, whereas pairing is the first rule of finding a square or a square root of any number.
Factors of 120 are 2^3 × 3^1 × 5^1.
Here we see that each prime number needs one more power to become a pair so we increase each of their's exponential powers by one and get 2^4 × 3^2 × 5^2 which is equal to 3600.
And therefore we conclude that the smallest square number divisible by 8, 15 and 20 is 3600, which is the square of 60.