Question

Find the least square number exactly divisible by each one of the numbers 6, 9, 12, 15,

and 18.

Answer 1

Given numbers = 6, 9, 15 and 20

The smallest number divisible by 6, 9, 15 and 20 is their L.C.M. i.e. 180

Resolving the L.C.M. as prime factors we get, 180= 2 × 2 × 3 × 3 × 5

To make it perfect square multiply by 5 then it becomes, 180= 2 × 2 × 3 × 3 × 5 × 5

Which implies 180 × 5 = 900

Least square number which is exactly divisible by 6, 9, 15 and 20 is 900.