first chern class

Question

If $M$ is a Fano manifold, and $K_M$ is the canonical line bundle of $M$. If $L$ is an ample line bundle over $M$, and $c_1(L)=\lambda c_1(M)$, for some positive number $\lambda$. What is the relation of $L$ and $-K_M$? Of course, if $M$ is $\mathbb{CP}^n$, this is clear for $\lambda\in Z^+$, how about other cases? Furthermore, what is the relation of the divisors with respect to $L$ and $-K_M$?