Let \(A = \{1, 2, 3, \ldots, 20\}\) be the set of the first 20 positive integers. For each \(X\) that is a 15-element subset of \(A\), let \(p(X)\) be the product of its elements. What is the maximum integer \(n\) such that \(n\) divides \(p(X)\) for all choices of \(X\)?

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