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3600 is the smallest perfect square divisible by 8,9 and 10.
Work out the prime factorisations for each of the numbers 8, 9, 10:
8 = 23
9 = 32
10 = 2 x 5
So the perfect square must be a multiple of the lcm of 8, 9 & 10 = 23 x 32 x 5 to be divisible by all three numbers.
All perfect squares have even powers for all their primes (in their prime factorisation), so to make all the powers even the smallest multiplier of this is 2 x 5, giving 24 x 32 x 52 = 3600.
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