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\( 120 × 2 × 3 × 5 = 3600\)