# Are you smarter than me? 47

Discrete Mathematics Level 4

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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