Check: $a = 675$, $b = 1350$, $\gcd(675, 1350) = 675$. Can we do better? Try $m + n = 2$: $d = 2025/2 = 1012.5$, not integer. Next smallest $m + n = 3$ gives $d = 675$. Any larger $m + n$ gives smaller $d$. So the maximum possible $\gcd(a, b)$ is $\boxed675$. - Nelissen Grade advocaten