MathNet 2025 — Part 01 (100 complete bilingual questions) Question 36

The product $abc$ of positive integers $a$, $b$, and $c$ is divisible by $3$, and the equations $a = \frac{b^2}{2} = \frac{c}{4}$ hold. Find the smallest possible sum of the numbers $a$, $b$, and $c$ under these conditions.