Find all triples $(a,b,c)$ of positive integers such that $(1+\frac{1}{a})(1+\frac{1}{b})(1+\frac{1}{c})=3$
Let $a,b,c$ positive integers such that $\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right) = 3$. Find those triples.