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We studied the minimum latency gossiping (all-to-all broadcast) problem in multihop radio networks defined as follows: Each node in the network is preloaded with a message and the objective is to distribute each node's message to the entire network with minimum latency. We studied this problem in the unit-size message model and the unit disk graph model. The unit-size model means different messages cannot be combined as one message, and the unit disk graph model means a link exists between two nodes if and only if their euclidean distance is less than 1. The minimum latency gossiping problem is known to be NP-hard in these two models. In this work, we designed a gossiping scheme that significantly improved all current gossiping algorithms in terms of the approximation ratio. Our work has approximation ratio 27, a great improvement of the current state-of-the-art algorithm (which has ratio 1,947). We also discussed the single point of failure problem and its impact on our approximation ratio. We designed an amended gossiping algorithm with ratio 27 in case of a nonsource node failure. We also designed an amended gossiping algorithm with ratio 29 in case of source failure.