# Did you say "maximum"? Oh, come on!

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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