Large Language Models (LLMs) herald a transformative era in artificial intelligence (AI). However, the expansive scale of data and parameters of LLMs requires high-demand computational and memory resources, restricting their accessibility to a broader range of users and researchers. This paper introduces an effective approach that enhances the operational efficiency and affordability of LLM inference. By utilizing transformer-based federated learning (FL) with model-parallel distributed training, our model efficiently distributes the computational loads and memory requirements across a network of participants. This strategy permits users, especially those with limited resources to train state-of-the-art LLMs collaboratively. We also innovate an incentive mechanism within the FL framework, rewarding constructive contributions and filtering out malicious activities, thereby safeguarding the integrity and reliability of the training process. Concurrently, we leverage memory hierarchy strategies and Singular Value Decomposition (SVD) on weight matrices to boost computational and memory efficiencies further. Our results, derived from formulaic analyses and numerical calculations, demonstrate significant optimization of resource use and democratize access to cutting-edge LLMs, ensuring that a wide scale of users can both contribute to and benefit from these advanced models.