Question

Find the least square number, exactly divisible by each one of the number: 

8, 12, 15 and 20

Answer 1

 The smallest number divisible by 8, 12, 15 and 20 is their L.C.M., which is equal to 120.
Factorising 120 into its prime factors:
120 = 2 x 2 x 2 x 3 x 5
Grouping them into pairs of equal factors:
120 = (2 x 2) x 2 x 3 x 5
The factors 2, 3 and 5 are not paired. To make 120 into a perfect square, we have to multiply it by 2 x 3 x 5, i.e. by 30.
The perfect square is 120 x 30, which is equal to 3600.