Need answer quickly Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
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What is the smallest square number that is divisible by 8, 15, and 20?
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First, let’s factor each of the proposed divisors into its prime factors:
8 = 2 * 2 * 2, 15 = 3 * 5, and 20 = 2 * 2 * 5. The least common multiple (LCM) is then
2 * 2 * 2 * 3 * 5 = 120. Now, any square that is evenly divisible by 8, 15, and 20 has
to be divisible by the LCM and any of its multiples. The multiple we want is the
smallest square, which can be generated by including an even number of each of
the factors in the prime factorization, namely 2 * 2 * 2 (* 2) *3 (* 3) *5 (* 5) or 120
(the LCM) * ( 2 * 3 * 5) = 120 * 30 = 3600.
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So, smallest square number that is divisible by 8, 15 and 20 is 3600.
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