In our era of widespread false information, human fact-checkers often face the challenge of duplicating efforts when verifying claims that may have already been addressed in other countries or languages. As false information transcends linguistic boundaries, the ability to automatically detect previously fact-checked claims across languages has become an increasingly important task. This paper presents the first comprehensive evaluation of large language models (LLMs) for multilingual previously fact-checked claim detection. We assess seven LLMs across 20 languages in both monolingual and cross-lingual settings. Our results show that while LLMs perform well for high-resource languages, they struggle with low-resource languages. Moreover, translating original texts into English proved to be beneficial for low-resource languages. These findings highlight the potential of LLMs for multilingual previously fact-checked claim detection and provide a foundation for further research on this promising application of LLMs.