Achieving consensus in group decision-making often involves overcoming significant challenges, particularly in reconciling diverse perspectives and mitigating biases that hinder agreement. Traditional methods relying on human facilitators are often constrained by scalability and efficiency, especially in large-scale, fast-paced discussions. To address these challenges, this study proposes a novel framework employing large language models (LLMs) as automated facilitators within a custom-built multi-user chat system. Leveraging cosine similarity as a core metric, this approach evaluates the ability of three state-of-the-art LLMs- ChatGPT 4.0, Mistral Large 2, and AI21 Jamba Instruct- to synthesize consensus proposals that align with participants' viewpoints. Unlike conventional techniques, the system integrates adaptive facilitation strategies, including clarifying misunderstandings, summarizing discussions, and proposing compromises, enabling the LLMs to iteratively refine consensus proposals based on user feedback. Experimental results demonstrate the superiority of ChatGPT 4.0, which achieves higher alignment with participant opinions, requiring fewer iterations to reach consensus compared to its counterparts. Moreover, analysis reveals the nuanced performance of the models across various sustainability-focused discussion topics, such as climate action, quality education, good health and well-being, and access to clean water and sanitation. These findings highlight the transformative potential of LLM-driven facilitation for improving collective decision-making processes and underscore the importance of advancing evaluation metrics and cross-cultural adaptability in future research.