For multiple integrated energy systems with similar energy using behavior, the federated learning mechanism can build a higher precision multivariate load prediction model for each integrated energy system. However, the data of different loads in these systems often have different time scales, limited by the characteristics and frequency of data acquisition equipment. Systems often set different hyperparameters with each other to ensure prediction accuracy, which makes it difficult to use federated learning for co-training. In this paper, a multi-stage Long Short-Term Memory (LSTM) federated model based on interpolation method is proposed for multi-node multivariate load forecasting on multi-time scales. In the first stage, the load data of larger time scales are interpolated to unify all the load data to the same time scale. In the second stage, each node (i.e., each integrated energy system) uses its own data to carry out multivariate load training and establish its multivariate load forecasting model. In the third stage, based on the federated learning mechanism and fine-tuning strategy, the LSTM federated prediction of multiple loads is established by fusion training between nodes. Experimental results show that the proposed method can obtain higher precision multi-source load prediction results for multiple integrated energy systems.