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 $180 \times 5 = 900$