Question

Find the least square number exactly divisible by each one is equal to the number 6, 9, 15 and 20.

Answer 1

First we find least number which is exactly divisible by numbers $6,9,15$ and $20$

For that we need to find LCM

$6=2\times 3$

$9=3\times 3$

$15=3\times 5$

$20=2\times 2\times 5$

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

LCM $=2^2\times 3^2\times 5$

To make it perfect square we need to multiply it by $5=2^2\times 3^2\times 5^2={30}^2=900$

$\therefore 900$ is the least square number which is exactly divisible by each of the numbers $6,9,15$ and $20$