MathNet 2015-part-01 — 191 problems (EN–VI) Question 10

Find all $n \in \mathbb{N}$ that can be represented in the form $n = [a,b] + [b,c] + [c,a]$ with $a, b, c \in \mathbb{N}$. Here $[u,v]$ denotes the least common multiple of $u$ and $v$.