Does Egyptian fraction help?

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

Let nn be an integer greater than 2017 and a,b,ca, b, c be distinct pairwise coprime positive integers satisfying the equation above.

What is the least possible value of n?n?

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