Question

Find the smallest square number divisible by each one of the numbers $4$, $9$ and $10$

Answer 1

Step 1: Find the LCM

Given numbers are $4$, $9$ and $10$

Prime factors of $4$ are

$4=2\times 2$

Prime factors of $9$ are

$9=3\times 3$

Prime factors of $10$ are

$10=5\times 2$

$\therefore$LCM of $4$, $9$ and $10$

LCM$\left(4,9,10\right)=\times 2\times 2\times 3\times 3\times 5=180$

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

On grouping the factors of $180$, we get

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

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

So, to make it perfect square, $180$ must be multiplied with $5$

$\therefore 180\times 5=900$

Hence, $900$ is the smallest square number divisible by each one of the numbers $4$, $9$ and $10$