Question

Find the smallest square number that is divisible by each of the numbers \(4, 9\), and \(10\).

Answer 1

The number that will be perfectly divisible by each one of \(4, 9\), and \(10\) is their LCM. 
The LCM of these numbers is as follows. 

2	4,9,10
2	2,9,5
3	1,9,5
3	1,3,5
5	1,1,5
	1,1,1

LCM of \(4, 9, 10\) = \(\underline{2 × 2} × \underline{3 × 3} × 5 =180\)
Here, prime factor \(5\) does not have its pair. 
Therefore, \(180\) is not a perfect square. 
If we multiply \(180\) with \(5\), then the number will become a perfect square. 
Therefore, \(180\) should be multiplied with \(5\) to obtain a perfect square.

Hence, the required square number is \(180 \times 5 = 900\)