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

we know thatthe number that will be perfectly divisible by each one of 4, 9, and 10 is their LCM.

The LCM of these numbers is:

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