Broadcast is an essential and widely used operation in multihop wireless networks. Minimum latency broadcast scheduling (MLBS) aims to find a collision-free scheduling for broadcast with the minimum latency. Previous work on MLBS mostly assumes that nodes are always active, and, thus, is not suitable for duty-cycled scenarios. In this paper, we investigate the MLBS problem in duty cycled multihop wireless networks (MLBSDC problem). We prove both the one-to-all and the all-to-all MLBSDC problems to be NP hard. We propose a novel approximation algorithm called OTAB for the one-to-all MLBSDC problem, and two approximation algorithms called UTB and UNB for the all-to-all MLBSDC problem under the unit-size and the unbounded-size message models, respectively. The approximation ratios of the OTAB, UTB, and UNB algorithms are at most 17|T|, 17|T| + 20, and (Δ + 22)|T|, respectively, where |T| denotes the number of time slots in a scheduling period, and Δ denotes the maximum node degree of the network. The overhead of our algorithms is at most constant times as large as the minimum overhead in terms of the total number of transmissions. We also devise a method called Prune to further reduce the overhead of our algorithms. Extensive simulations are conducted to evaluate the performance of our algorithms.