Practice (101)
A rectangular box measures $a \times b \times c$, where $a$, $b$, and $c$ are integers and $1\leq a \leq b \leq c$. The volume and the surface area of the box are numerically equal. How many ordered triples $(a,b,c)$ are possible?
The sum of the three different positive unit fractions is $\frac{6}{7}$. What is the least number that could be the sum of the denominators of these fractions?