Large language models (LLMs) possess extensive world knowledge, yet methods for effectively eliciting this knowledge remain underexplored. Nationality and region prediction tasks require understanding of not only linguistic features but also cultural and historical background, making LLM world knowledge particularly valuable. However, conventional LLM prompting methods rely on direct reasoning approaches, which have limitations in applying abstract linguistic rules. We propose LLM Associative Memory Agents (LAMA), a novel framework that leverages LLM world knowledge as associative memory. Rather than directly inferring nationality from names, LAMA recalls famous individuals with the same name and aggregates their nationalities through indirect reasoning. A dual-agent architecture comprising a Person Agent and a Media Agent, specialized in different knowledge domains, recalls famous individuals in parallel, generating Top-1 predictions through voting and Top-K predictions through conditional completion. On a 99-country nationality prediction task, LAMA achieved 0.817 accuracy, substantially outperforming conventional LLM prompting methods and neural models. Our experiments reveal that LLMs exhibit higher reliability in recalling concrete examples than in abstract reasoning, that recall-based approaches are robust to low-frequency nationalities independent of data frequency distributions, and that the dual-agent architecture functions complementarily to produce synergistic effects. These results demonstrate the effectiveness of a new multi-agent system that retrieves and aggregates LLM knowledge rather than prompting reasoning.