Question

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

Answer 1

The number that is perfectly divisible by each of the numbers $8, 15$, and $20$ is their LCM.

2	8,15,20
2	4,15,10
2	2,15,5
3	1,15,5
5	1,5,5
1,1,1

LCM of $8, 15$, and $20$ =$\underline{ 2 × 2} × 2 × 3 × 5 =120$
Here, prime factors $2, 3,$ and $5$ do not have their respective pairs.
Therefore, $120$ is not a perfect square.
Therefore, $120$ should be multiplied by $2 × 3 × 5,$i.e. $30$, to obtain a perfect square.

Hence, the required square number is$120 × 2 × 3 × 5 = 3600$