NO-ABEL 2014 Problem 4

Find all triples $(a, b, c)$ of positive integers for which $\frac{32a + 3b + 48c}{4abc}$ is also an integer.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.