2009 AMC 8 Problems/Problem 17

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Problem

The positive integers $x$ and $y$ are the two smallest positive integers for which the product of $360$ and $x$ is a square and the product of $360$ and $y$ is a cube. What is the sum of $x$ and $y$?

$\textbf{(A)}\   80    \qquad \textbf{(B)}\    85   \qquad \textbf{(C)}\    115   \qquad \textbf{(D)}\    165   \qquad \textbf{(E)}\    610$

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