Longitudinal cluster randomized trial (LCRT) is one type of cluster randomized trials, which has been frequently used in clinical research. In LCRTs, clusters of subjects are randomly assigned to di?erent treatment groups and each subject has repeated measurements over the time during the study. These features, however, present challenges that need to be addressed in experimental design and data analysis stages. One salient feature of LCRTs is the complicated correlation structure constituted by longitudinal and between-subject correlations. To handle them, we propose closed-form sample size and power formulas for detecting the intervention e?ect between two treatment groups for LCRTs with binary outcomes, which offers great flexibility to account for unbalanced design, di?erent missing patterns and complicated correlation structures. Extensive simulation studies show that the proposed methods achieve good performance.