Clustered federated learning (CFL) addresses the performance challenges posed by data heterogeneity in federated learning (FL) by organizing edge devices with similar data distributions into clusters, enabling collaborative model training tailored to each group. However, existing CFL approaches strictly limit knowledge sharing to within clusters, lacking the integration of global knowledge with intra-cluster training, which leads to suboptimal performance. Moreover, traditional clustering methods incur significant computational overhead, especially as the number of edge devices increases. In this paper, we propose LCFed, an efficient CFL framework to combat these challenges. By leveraging model partitioning and adopting distinct aggregation strategies for each sub-model, LCFed effectively incorporates global knowledge into intra-cluster co-training, achieving optimal training performance. Additionally, LCFed customizes a computationally efficient model similarity measurement method based on low-rank models, enabling real-time cluster updates with minimal computational overhead. Extensive experiments show that LCFed outperforms state-of-the-art benchmarks in both test accuracy and clustering computational efficiency.