This research aims to develop a dynamic and scalable framework to facilitate harmonization of Common Data Elements (CDEs) across heterogeneous biomedical datasets by addressing challenges such as semantic heterogeneity, structural variability, and context dependence to streamline integration, enhance interoperability, and accelerate scientific discovery. Our methodology leverages Large Language Models (LLMs) for context-aware text embeddings that convert CDEs into dense vectors capturing semantic relationships and patterns. These embeddings are clustered using Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) to group semantically similar CDEs. The framework incorporates four key steps: (1) LLM-based text embedding to mathematically represent semantic context, (2) unsupervised clustering of embeddings via HDBSCAN, (3) automated labeling using LLM summarization, and (4) supervised learning to train a classifier assigning new or unclustered CDEs to labeled clusters. Evaluated on the NIH NLM CDE Repository with over 24,000 CDEs, the system identified 118 meaningful clusters at an optimized minimum cluster size of 20. The classifier achieved 90.46 percent overall accuracy, performing best in larger categories. External validation against Gravity Projects Social Determinants of Health domains showed strong agreement (Adjusted Rand Index 0.52, Normalized Mutual Information 0.78), indicating that embeddings effectively capture cluster characteristics. This adaptable and scalable approach offers a practical solution to CDE harmonization, improving selection efficiency and supporting ongoing data interoperability.