MathNet 2024-part-04 — 168 problems (EN–VI) Question 68

Determine all positive integers $a, b, c, d, e, f$ satisfying the following condition: for any two of them, $x$ and $y$, two of the remaining four numbers, $z$ and $t$, exist such that $\frac{x}{y} = \frac{z}{t}$.