Find the least square number which is exactly divisible by

Question:

Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.

Solution:

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

L.C.M. of 6, 9, 15, 20 = 180

Resolving into prime factors: 

$180=2 \times 2 \times 3 \times 3 \times 5$

To make it a perfect square, we multiply it with 5.

Required number $=180 \times 5=900$

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