Does Egyptian fraction help?

\[\dfrac{2017}{n} = \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}\]

Let \(n\) be an integer greater than 2017 and \(a, b, c\) be distinct pairwise coprime positive integers satisfying the equation above.

What is the least possible value of \(n\)?

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