Federated Learning (FL) is a prevalent machine learning paradigm designed to address challenges posed by heterogeneous client data while preserving data privacy. Unlike distributed training, it typically orchestrates resource-constrained edge devices to communicate via a low-bandwidth communication network with a central server. This urges the development of more computation and communication efficient training algorithms. In this paper, we propose an efficient FL paradigm, where the local models in the clients are trained with low-precision operations and communicated with the server in low precision format, while only the model aggregation in the server is performed with high-precision computation. We surprisingly find that high precision models can be recovered from the low precision local models with proper aggregation in the server. In this way, both the workload in the client-side and the communication cost can be significantly reduced. We theoretically show that our proposed paradigm can converge to the optimal solution as the training goes on, which demonstrates that low precision local training is enough for FL. Our paradigm can be integrated with existing FL algorithms flexibly. Experiments across extensive benchmarks are conducted to showcase the effectiveness of our proposed method. Notably, the models trained by our method with the precision as low as 8 bits are comparable to those from the full precision training. As a by-product, we show that low precision local training can relieve the over-fitting issue in local training, which under heterogeneous client data can cause the client models drift further away from each other and lead to the failure in model aggregation.