Question

Find the smallest square number divisible by each one of the numbers $8,$$15$ and $20$

Answer 1

Step 1: Find the LCM

Given numbers are $8,$$15$ and $20$

Prime factors of $8$ are

$8=2\times 2\times 2$

Prime factors of $15$ are

$15=3\times 5$

Prime factors of $20$ are

$20=5\times 2\times 2$

$\therefore$LCM of $8,$$15$ and

LCM$\left(8,15,20\right)=2\times 2\times 2\times 3\times 5=120$

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

On grouping the factors of $120$, we get

$120=(2\times 2)\times 2\times 3\times 5$

That is $2$, $3$ and $5$ is not able to make their pair.

So, to make it perfect square, $120$ must be multiplied with $2\times 5\times 3=30$

$\therefore 120\times 30=3600$

Hence, $3600$ is the smallest square number divisible by each one of the numbers $8,$$15$ and $20$