Fact-checking techniques can mitigate hallucinations in Large Language Models (LLMs), a prominent issue in specialized domains. As parameter-efficient techniques such as Low-Rank Adaptation (LoRA) can overcome substantial computational overhead, some studies have explored the integration of multiple LoRAs. While previous studies focus on parallel integration, this paper investigates methods to establish connections among multiple LoRAs. We create three reasoning datasets tailored to fact-checking and fine-tune individual LoRAs, allowing them to view and reason from diverse perspectives. Then, we explore strategies for allocating these reasoning LoRAs and introduce LoraMap, an approach to map connections between them. The results of the fact-checking task demonstrate that the performance of LoraMap is superior to LoraHub, an existing method for integrating LoRAs. LoraMap also outperforms with significantly fewer trainable parameters than LoraConcat, which concatenates LoRAs and further fine-tunes them.