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In this paper, we present CLCA, a novel framework for enhancing LLM alignment with cultural values based on cultural learning. The framework leverages simulated social interactions to generate conversations in which LLMs engage in role-playing within culturally adapted social scenarios, capturing implicit cultural norms for model fine-tuning. CLCA improves cultural value alignment across various model architectures measured using World Value Survey data, demonstrating the effectiveness of our proposed approach. 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