The SLAMMOT, i.e. simultaneous localization, mapping, and moving object (detection and) tracking, represents an emerging technology for autonomous vehicles in dynamic environments. Such single-vehicle systems still have inherent limitations, such as occlusion issues. Inspired by SLAMMOT and rapidly evolving cooperative technologies, it is natural to explore cooperative simultaneous localization, mapping, moving object (detection and) tracking (C-SLAMMOT) to enhance state estimation for ego-vehicles and moving objects. C-SLAMMOT could significantly upgrade the single-vehicle performance by utilizing and integrating the shared information through communication among the multiple vehicles. This inevitably leads to a fundamental trade-off between performance and communication cost, especially in a scalable manner as the number of collaboration vehicles increases. To address this challenge, we propose a LiDAR-based communication-efficient C-SLAMMOT (CE C-SLAMMOT) method by determining the number of collaboration vehicles. In CE C-SLAMMOT, we adopt descriptor-based methods for enhancing ego-vehicle pose estimation and spatial confidence map-based methods for cooperative object perception, allowing for the continuous and dynamic selection of the corresponding critical collaboration vehicles and interaction content. This approach avoids the waste of precious communication costs by preventing the sharing of information from certain collaborative vehicles that may contribute little or no performance gain, compared to the baseline method of exchanging raw observation information among all vehicles. Comparative experiments in various aspects have confirmed that the proposed method achieves a good trade-off between performance and communication costs, while also outperforms previous state-of-the-art methods in cooperative perception performance.