Suppose that n is a positive integer. We define the Smarandache function S(n) by specifying that S(n) is the least positive integer for which n divides S(n)!. For example, S(8) = 4 because 8 does not divide 1! = 1, 2! = 2, and 3! = 6, but it does divide 4! = 24.
Find S(n) for all positive integers n not exceeding 12.
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