I'm stuck on a pretty straightforward LM type of problem.

Here's the problem statement.

a,b,c are positive constants. x,y,z are positive and that ayz+bzx+cxy=3abc. Show that xyz =< abc.

So I've approached it by setting f(x,y,z)=xyz subject to ayz+bzx+cxy=3abc

so F(x,y,z,lamda)=xyz-lamda(ayz+bzx+cxy-3abc)

then I kinda got lost...

Any pointers? Thanks.