3D multi-person motion prediction is a highly complex task, primarily due to the dependencies on both individual past movements and the interactions between agents. Moreover, effectively modeling these interactions often incurs substantial computational costs. In this work, we propose a computationally efficient model for multi-person motion prediction by simplifying spatial and temporal interactions. Our approach begins with the design of lightweight dual branches that learn local and global representations for individual and multiple persons separately. Additionally, we introduce a novel cross-level interaction block to integrate the spatial and temporal representations from both branches. To further enhance interaction modeling, we explicitly incorporate the spatial inter-person distance embedding. With above efficient temporal and spatial design, we achieve state-of-the-art performance for multiple metrics on standard datasets of CMU-Mocap, MuPoTS-3D, and 3DPW, while significantly reducing the computational cost. Code is available at https://github.com/Yuanhong-Zheng/EMPMP.