If $A,B \in \mathbb{R}^{7 \times 7}, \operatorname{rank}(A) = 4, \operatorname{rank}(B) = 5$, what's range of $ \operatorname{rank}(AB)$?

Question

I know that the upper bound is $\min(\operatorname{rank}(A), \operatorname{rank}(B))$, but how do I obtain the lower bound?