LLM-based multi-agent systems (MAS) increasingly use latent collaboration to avoid the information loss and repeated encoding-decoding overhead of natural-language communication. However, directly forwarding all sender latents makes the receiver-side context scale with both the number of agents and the reasoning length, increasing computation, memory usage, and collaboration latency. A natural solution is latent compression. But we find that cross-agent redundancy remains unresolved in existing latent compression approaches, which typically compress each sender independently and then concatenate the results. We propose LatCom, a cross-agent latent compression framework for efficient multi-agent latent collaboration. LatCom maps multiple sender latents into a fixed number of receiver-readable and task-relevant slots. Rather than reconstructing all sender hidden states, it optimizes the compressed latents for receiver-side task utility. LatCom trains the compressor in two stages: single-sender readability learning first establishes a latent interface interpretable by the frozen receiver, and multi-sender fusion learning then trains the compressor to fuse complementary evidence and remove redundancy across agents. Experiments on multiple benchmarks with the Qwen-4B model show that LatCom improves average inference speed by 2.46x over LatentMAS, reduces token usage by 70.3%, and increases average accuracy by 0.46%.