Question

Find the smallest square number divisible by each one of the numbers $8,9$ and $10$

Answer 1

Step 1: Find the LCM

Given numbers are $8,9$ and $10$

Prime factors of $8$ are

$8=2\times 2\times 2$

Prime factors of $9$ are

$9=3\times 3$

Prime factors of $10$ are

$10=5\times 2$

$\therefore$LCM of $8,9$ and $10$

LCM$\left(8,9,10\right)=2\times 2\times 2\times 3\times 3\times 5=360$

Step 2: Find the least square no divisible by given numbers

On grouping the factors of $360$, we get

$360=(2\times 2)\times 2\times (3\times 3)\times 5$

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

So, to make it perfect square, $360$ must be multiplied with $2\times 5=10$

$\therefore 360\times 10=3600$

Hence, $3600$ is the smallest square number divisible by each one of the numbers $8,9$ and $10$