# Problem 1. (2 points)

Let $x, y, z$ be pairwise coprime three-digit natural numbers. What is the greatest value that the GCD $(x+y+z, x y z)$ can take?
Answer: 2994

Solution:

The GCD of two numbers cannot be greater than either of them. The maximum possible value of $x+$ $y+z=997+998+999=2994$ and for these numbers, $x y z$ is indeed divisible by $x+y+z=2994=3 \cdot 998$.