Question

how to find least perfect cube number that is divisible by 3, 8, 12 and 20

Answer 1

to find perfect cube number do the following:
knowing that

8 = 2^3
12 = 2^2 * 3
15 = 3 * 5
20 = 2^2 * 5

then ANY square that is divisible by all four must contain at least the factors 2^3 * 3^2 * 5^2. since all the prime factors of a square must have even exponents, the smallest therefore of such square is 2^4 * 3^2 * 5^2 = 3600.

Answer 2

Here is your answer,
8=2^4
12=2^2*3
15=3*5
18=3^2*3
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here =2^4*5^3*2^3=
=3600