# How many two-digit numbers are divisible by both 2 and 3?

$75$ numbers are divisible by $2$ and $3$.
The two digit numbers are $10$ to $99$. So there are $90$ two digit numbers. Half of them are even, so $45$ two digit numbers are divisible by $2$.
The lowest two digit number divisible by $3$ is $12$. And out of $90$ numbers, every $3$ is divisible by $3$. So there are $30$ two digit number divisible by $3$.
So $45 + 30 = 75$.