Conditional Probability, Independence & Bayes · Superchallenge problem

For a positive integer $n$, an integer $X$ is chosen uniformly at random from $\{1,2,\dots,n\}$. Let $A$ be the event that $X$ is even and $B$ the event that $X$ is a multiple of $3$. For how many $n$ with $1\le n\le100$ are $A$ and $B$ independent, that is, $P(A\cap B)=P(A)\,P(B)$?