MathNet 2017-part-07 — 172 problems (EN–VI) Question 103

Given that $a, b, c$ are integers with $a b c = 60$, and that complex number $\omega \neq 1$ satisfies $\omega^{3} = 1$, find the minimum possible value of $\left| a + b \omega + c \omega^{2} \right|$.