JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Permutations and Combinations

There are $900$ three-digit numbers. Those divisible by $3$ number $300$, those divisible by $4$ number $225$, and those divisible by $12$ number $75$, so by inclusion and exclusion $300+225-75=450$ are divisible by $3$ or $4$. Every multiple of $48$ is a multiple of both $3$ and $4$, and there are $18$ three-digit multiples of $48$. Removing them leaves $450-18=432$.