Let $K,L$ over $Q$ be field extension of prime degrees. Prove if $[KL:Q]<[K:Q][L:Q]$, then the Galois closure of $K/Q$ is the Galois closure of $L/Q$.

Question

Let $K$ and $L$ over $Q$ be field extension of prime degrees. Prove that if $[KL:Q]<[K:Q][L:Q]$, then the Galois closure of $K/Q$ equals to the Galois closure of $L/Q$.

I know the two extensions must be simple extensions, and the two degrees are equal. But I cannot figure out the rest.