proof compactness of sets

Question

Let $$K ⊂ R^m$$ and $$L ⊂ R^n$$ be compact subsets.

Show:

a) The set $$ K × L: = \{(x, y): x ∈ K, y ∈ L\} ⊂ R^{m+n}$$ is also compact.

I have to show that this is bounded and closed. But how do I do that?