Example 3. Given three different positive numbers, the sum of their reciprocals is
1. Try to find these three numbers.
Let the three numbers be $\mathrm{a}>\mathrm{b}>\mathrm{c}>1$, then $-\frac{1}{a}+\frac{1}{b}+\frac{1}{\mathrm{c}}$ $<\frac{3}{c}$, i.e., $c<3$. Therefore, $c=2, \frac{1}{a}+\frac{1}{b}=\frac{1}{2} . \because \frac{1}{a}+\frac{1}{b}$ $<\frac{2}{b}, \therefore b<4$, hence $\mathrm{b}=3$. From this, we get $\mathrm{a}=6$.