Educators evaluate student knowledge using knowledge component (KC) models that map assessment questions to KCs. Still, designing KC models for large question banks remains an insurmountable challenge for instructors who need to analyze each question by hand. The growing use of Generative AI in education is expected only to aggravate this chronic deficiency of expert-designed KC models, as course engineers designing KCs struggle to keep up with the pace at which questions are generated. In this work, we propose KCluster, a novel KC discovery algorithm based on identifying clusters of congruent questions according to a new similarity metric induced by a large language model (LLM). We demonstrate in three datasets that an LLM can create an effective metric of question similarity, which a clustering algorithm can use to create KC models from questions with minimal human effort. Combining the strengths of LLM and clustering, KCluster generates descriptive KC labels and discovers KC models that predict student performance better than the best expert-designed models available. In anticipation of future work, we illustrate how KCluster can reveal insights into difficult KCs and suggest improvements to instruction. [For the complete proceedings, see ED675583.]