Is the statement below sometimes, always, or never true? Give at least two examples to support your reasoning. The LCM of two square numbers is another square number.

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Mathematics

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4 June, 20:55

Is the statement below sometimes, always, or never true? Give at least two examples to support your reasoning. The LCM of two square numbers is another square number.

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Answers (1)

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Bailey Fields · Answer 1

Always true.

Step-by-step explanation:

A squared number will always have paired prime factors. When they have no prime factors in common, like 4 (2 x 2) and 9 (3 x 3), the LCM will be their product, 2 x 2 x 3 x 3 or 36 (6 squared). When they have prime factors in common, like 36 (2 x 2 x 3 x 3) and 225 (3 x 3 x 5 x 5), the LCM will still have paired factors: 2 x 2 x 3 x 3 x 5 x 5 or 900 (30 squared)