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

This math topic involves evaluating whether a given number \( z, r, y, b, m, r, \) or \( c \) is a multiple of two other specified numbers using prime factorization and variable exponents. Each question presents expressions where a number is expressed through a multiplication of primes raised to certain powers, and the student must determine if this number is a multiple of two others listed. This involves skills related to factoring, recognizing multiples, and working with lowest common multiples. Each question provides two answer choices: "Yes" or "No."

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Is Number a Multiple of Both - From Variables as Factors

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Is p a multiple of both 154 and 30?

p=2⋅3⋅5⋅7154=2⋅7⋅1130=2⋅3⋅5is p a multiple of 154 and 30?\begin{align*}p &= 2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]154 &= 2 \cdot 7 \cdot 11\\[-0.5em]30 &= 2 \cdot 3 \cdot 5\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\154\textsf{ and }30?