Mobile ad hoc networks (MANETs) have recently gained increased interest due to the widespread use of smart mobile devices. Group communication applications, serving for better cooperation between subsets of business members, become more significant in the context of MANETs. Multicast routing mechanisms are very useful communication techniques for such group-oriented applications. This paper deals with multicast routing problems in terms of stability and scalability, using the concept of stable core. We propose LMRSC (Lightweight Multicast Routing Based on Stable Core), a lightweight multicast routing technique for MANETs, in order to avoid periodic flooding of the source messages throughout the network, and to increase the duration of multicast routes. LMRSC establishes and maintains mesh architecture for each multicast group member by dividing the network into several zones, where each zone elects the most stable node as its core. Node residual energy and node velocity are used to calculate the node stability factor. The proposed algorithm is simulated by using NS-2 simulation, and is compared with other multicast routing mechanisms: ODMRP and PUMA. Packet delivery ratio, multicast route lifetime, and control packet overhead are used as performance metrics. These metrics are measured by gradual increase of the node mobility, the number of sources, the group size and the number of groups. The simulation performance results indicate that the proposed algorithm outperforms other mechanisms in terms of routes stability and network density.