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

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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

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