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 = 2 × 2 × 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 × 5 = 900