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

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

From the Brazilian Maths Olympiads (OBM) 2013.
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