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Q)

Find the least perfect square divisible by each one of 8 9 10

Find the least perfect square divisible by each one of 8 9 10

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A)

 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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