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Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.

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The number that is perfectly divisible by each of the numbers 8, 15, and 20 is their LCM.

2 8, 15, 20
2 4, 15, 10
2 2, 15, 5
3 1, 15, 5
5 1, 5, 5
1, 1, 1

LCM of 8, 15, and 20 = 2 × 2 × 2 × 3 × 5 =120

Here, prime factors 2, 3, and 5 do not have their respective pairs. Therefore, 120 is not a perfect square.

Therefore, 120 should be multiplied by 2 × 3 × 5, i.e. 30, to obtain a perfect square.

Hence, the required square number is 120 × 2 × 3 × 5 = 3600

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