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Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 2)

This math topic involves applying prime factorization to determine if one number is a multiple of two others. Problems require the use of factoring skills to break numbers down into their prime factors, and an understanding of multiples to determine the relationship between numbers. The central theme of these problems is to assess whether a given number, after its prime factors have been exposed, is a multiple of both of two other factored numbers simultaneously, which is part of practicing Lowest Common Multiple calculation. Each question displays the prime factorization of three numbers and asks if the first is a multiple of the other two.

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Is Number a Multiple of Both - From Values as Factors

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Is 84 a multiple of both 28 and 42?

84=22⋅3⋅728=22⋅742=2⋅3⋅7is 84 a multiple of 28 and 42?\begin{align*}84 &= 2^2 \cdot 3 \cdot 7\\[-0.5em]28 &= 2^2 \cdot 7\\[-0.5em]42 &= 2 \cdot 3 \cdot 7\end{align*}\\\\ \textsf{is }84\textsf{ a multiple of }\\28\textsf{ and }42?