Conditional Probability, Independence & Bayes · Superchallenge problem

An integer is chosen uniformly at random from $\{1,2,\ldots,n\}$. Let $A$ be the event that it is divisible by $3$ and $B$ the event that it is divisible by $4$. For how many values of $n$ with $1\le n\le100$ are $A$ and $B$ independent, that is, $P(A\cap B)=P(A)\,P(B)$?