Language Reduction for any Language Given two languages $L_1$ and $L_2$, give a language $L'$ that both $L_1$ and $L_2$ reduce to.

I'm not quite how to do this. I know the solution is fairly simple. I know I can somehow represent $L'$ in terms of $L_1$ and $L_2$. Then I need to create a computable function that maps $L_1$ to $L'$ and either use the same function, or create a separate function that maps $L_2$ to $L'$.
Hint: Try $L=0L_1\cup1L_2$. Can you see how to map $L_1$ to $L$ and $L_2$ to $L$? You have to be slightly clever; you might want to use prefixes other than 0 and 1.