An increase in the deployment of Distributed Energy Resources (DERs) and Renewable Energy (RE) resources is a promising paradigm in the decentralized energy era. It has motivated multi-Microgrids (MGs) to trade energy directly with others in the Local Energy Market (LEM), as well as with the main grid. The LEM has become a popular platform that covers several shortcomings of surplus/deficient energy, which can also manage the increasing connection of multi-microgrids, meet internal balance, and maximize the social welfare of the community Microgrid (MG). Moreover, in the LEM, the MGs would like to provide some payoff to encourage each other to exchange their energy locally. However, designing an appropriate market framework, privacy protection, and the community's unbalanced energy supply and demand is challenging. To cope with these challenges, in this study, an LEM for a multimicrogrid system is designed to maximize the social welfare of the community, and a decentralized clearing algorithm based on the Alternating Direction Method of Multipliers (ADMM) is proposed for local market clearing and privacy protection. The Community Manager (CM) is used as an intermediate coordinator between the interconnected MGs. This way, the computation process will be completely distributed, and the privacy of each MG will be protected. Moreover, considering the utility function for the consumers and energy providers, an equivalent cost model based on internal pricing is proposed to state the willingness of the utility and motivate the participants to join LEM. Finally, an illustrative example and a case study are used to demonstrate the efficiency and effectiveness of the proposed design of LEM and algorithm in terms of social welfare and power balance. In our study, we found that by using dynamic pricing in conjunction with our proposed model, the social welfare of the energy community can be increased by 14.25%. This demonstrates the significant economic benefits and effectiveness of our approach in the Local Energy Market (LEM).INDEX TERMS Local energy market, Alternating direction method of multipliers, Multi-microgrids, Community manager, Energy transaction.