A counterexample to [LM:K] = [L:K] [M:K]

Question

I can't find a solution for the following task:

Let $F/K$ be a finite dimensional field extension with intermediate fields $L$ and $M$.

Use a real and non-real cube root of 2 to give an example where $L \cap M = K$ and $[L:K]=[M:K]=3$ ,but $[LM:K]<9$.

Thanks for any answers.