Are you smarter than me? 47

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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