In various work contexts, such as meeting scheduling, collaborating, and project planning, collective decision-making is essential but often challenging due to diverse individual preferences, varying work focuses, and power dynamics among members. To address this, we propose a system leveraging Large Language Models (LLMs) to facilitate group decision-making by managing conversations and balancing preferences among individuals. Our system extracts individual preferences and suggests options that satisfy a significant portion of the members. We apply this system to corporate meeting scheduling. We create synthetic employee profiles and simulate conversations at scale, leveraging LLMs to evaluate the system. Our results indicate efficient coordination with reduced interactions between members and the LLM-based system. The system also effectively refines proposed options over time, ensuring their quality and equity. Finally, we conduct a survey study involving human participants to assess our system's ability to aggregate preferences and reasoning. Our findings show that the system exhibits strong performance in both dimensions.