Tangled code changes, commits that conflate unrelated modifications such as bug fixes, refactorings, and enhancements, introduce significant noise into bug datasets and adversely affect the performance of bug prediction models. Addressing this issue at a fine-grained, method-level granularity remains unexplored. This is critical to address, as recent bug prediction models, driven by practitioner demand, are increasingly focusing on finer granularity rather than traditional class- or file-level predictions. This study investigates the utility of Large Language Models (LLMs) for detecting tangled code changes by leveraging both commit messages and method-level code diffs. We formulate the problem as a binary classification task and evaluate multiple prompting strategies, including zero-shot, few-shot, and chain-of-thought prompting, using state-of-the-art proprietary LLMs such as GPT-5 and Gemini-2.0-Flash, and open-source models such as GPT-OSS-120B and CodeBERT. Our results demonstrate that combining commit messages with code diffs significantly enhances model performance, with the combined few-shot and chain-of-thought prompting achieving an F1-score of 0.883. Additionally, we explore machine learning models trained on LLM-generated embeddings, where a multi-layer perceptron classifier achieves superior performance (F1-score: 0.906, MCC: 0.807). Applying our approach to 49 open-source projects improves the distributional separability of code metrics between buggy and non-buggy methods, demonstrating the promise of LLMs for method-level commit untangling and potentially contributing to improving the accuracy of future bug prediction models.