Find GCD!

Number Theory Level pending

\(x\) and \(y\) are two positive integers. The greatest common divisor (GCD) and lowest common multiple (LCM) of \(x^{2}y\) and \(xy^{2}\) are \(p\) and \(q\) respectively. If \(p^{2}=27q\), then what is the GCD of \(x\) and \(y\)?

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