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.

Question

Mathematics

Dj

15 November, 22:30

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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Alexandria Gilbert · 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)