Question

Find the smallest square number divisible by each one of the numbers $6$, $9$ and $15$

Answer 1

Step 1: Find the LCM

Given numbers are $6$, $9$ and $15$

Prime factors of $6$ are

$6=2\times 3$

Prime factors of $15$ are

$15=3\times 5$

Prime factors of $9$ are

$9=3\times 3$

$\therefore$LCM of $6$, $9$ and $15$

LCM$\left(6,9,15\right)=2\times 3\times 3\times 5=90$

Step 2: Find the least square number divisible by the given numbers

On grouping the factors of $90$, we get

$90=(3\times 3)\times 2\times 5$

That is $2$ and $5$ is not able to make their pair.

So, to make it perfect square, $90$ must be multiplied with $2\times 5=10$

$\therefore 90\times 10=900$

Hence, $900$ is the smallest square number divisible by each one of the numbers $6$,$9$ and $15$.