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In this paper, we discuss the minimum latency broadcast problem (MLB) in multi-channel multi-hop wireless networks (MLB-MC). This problem is NP-hard since its special version, MLB in single-channel network (MLB-SC) is proved to be NP-hard . We design an efficient approximation for MLB-MC, analyze its approximation ratio, and evaluate its performance via numerical experiments. Furthermore, we give a general theorem as an upper bound to compare the performance between approximations for MLB-MC and MLB-SC.