Constructing a reduction between two languages about pairs of Turing machines I'm curious about a potential relation between the following two languages.

$L_1 := \{\langle M_1, M_2 \rangle : L(M_1) \cap L(M_2) \ne \emptyset \}$.

$L_2  := \{\langle M_1, M_2 \rangle : L(M_1) \ne L(M_2) \}$.


  Is it true that $L_2$ mapping reduces to $L_1$?


I've had many failed attempts to construct a reduction and would appreciate any help.
Here are three hints. 


Show that $L_2$ is not computably enumerable.
Show that $L_1$ is computably enumerable.
If $L_2$ mapping reduces to $L_1$, what does it imply?