JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Permutations and Combinations

There are $999-99=900$ three-digit numbers in total.

Numbers divisible by both $2$ and $3$, i.e. by $6$: $\frac{900}{6}=150$.

Numbers divisible by both $4$ and $9$, i.e. by $\mathrm{lcm}(4,9)=36$ (every such number is automatically a multiple of $6$ too): $\frac{900}{36}=25$.

Removing these from the multiples of $6$: