Translating conversational text, particularly in customer support contexts, presents unique challenges due to its informal and unstructured nature. We propose a context-aware LLM translation system that leverages conversation summarization and dialogue history to enhance translation quality for the English-Korean language pair. Our approach incorporates the two most recent dialogues as raw data and a summary of earlier conversations to manage context length effectively. We demonstrate that this method significantly improves translation accuracy, maintaining coherence and consistency across conversations. This system offers a practical solution for customer support translation tasks, addressing the complexities of conversational text.