If three distinct positive integers \(\large\color{Royalblue}{a,b,c}\) with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer.

Find \(\large\color{Royalblue}{(a+b)-(abc+c)}\)

**Details and assumptions**

\(\large{a<b<c}\)

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