In this paper, we provide Routley-Meyer semantics for the many-valued logics ${L}C$ and LC, and give completeness for each of them. This result shows the following two: 1) Routley-Meyer semantics is very powerful in the sense that it can be used as the semantics for several sorts of logics, i.e., many-valued logic, not merely relevance logic and substructural logic. Note that each implication of ${L}C$ and LC does not (partially) result in "paradoxes of material implication" 2) This implies that Routley-Meyer semantics can be also used not merely for relevance systems but also for other logical systems such as ${L}C$ and LC, each of which has its own implication by which we can overcome (partially) the problem of "paradoxes of material implication".