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Omni-MATH / Let V be a rectangular prism with integer side lengths. The largest face has area 240 and the smallest face has area 48. A third face has area x, where x is not equal to 48 or 240.…

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problem

Let VV be a rectangular prism with integer side lengths. The largest face has area 240 and the smallest face has area 48. A third face has area xx, where xx is not equal to 48 or 240. What is the sum of all possible values of xx?
Plain-text mathematical notation (without MathML)
Let V be a rectangular prism with integer side lengths. The largest face has area 240 and the smallest face has area 48. A third face has area x, where x is not equal to 48 or 240. What is the sum of all possible values of x?
Original LaTeX notation
Let $V$ be a rectangular prism with integer side lengths. The largest face has area 240 and the smallest face has area 48. A third face has area $x$, where $x$ is not equal to 48 or 240. What is the sum of all possible values of $x$?

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