turkey-yks 2011 Q11

turkey-yks · Other · lys1-math Number Theory GCD, LCM, and Coprimality

Let p and q be distinct prime numbers such that
$$\begin{aligned} & a = p ^ { 4 } \cdot q ^ { 2 } \\ & b = p ^ { 2 } \cdot q ^ { 3 } \end{aligned}$$
Which of the following is the greatest common divisor of numbers a and b?
A) $p ^ { 5 } \cdot q ^ { 4 }$
B) $p ^ { 4 } \cdot q ^ { 3 }$
C) $p ^ { 3 } \cdot q ^ { 4 }$
D) $p ^ { 2 } \cdot q ^ { 2 }$
E) $p ^ { 2 } \cdot q ^ { 3 }$

Let p and q be distinct prime numbers such that

$$\begin{aligned}
& a = p ^ { 4 } \cdot q ^ { 2 } \\
& b = p ^ { 2 } \cdot q ^ { 3 }
\end{aligned}$$

Which of the following is the greatest common divisor of numbers a and b?\\
A) $p ^ { 5 } \cdot q ^ { 4 }$\\
B) $p ^ { 4 } \cdot q ^ { 3 }$\\
C) $p ^ { 3 } \cdot q ^ { 4 }$\\
D) $p ^ { 2 } \cdot q ^ { 2 }$\\
E) $p ^ { 2 } \cdot q ^ { 3 }$

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