A Simplified Enumeration Strategy for Understanding LCM and GCF

In elementary mathematics, it is essential to comprehend the Least Common Multiple (LCM) and Greatest Common Factor (GCF). However, many students find traditional methods difficult because of excessive listing, memorization, and cognitive overload. The Ascending Multiple Check Method for determining LCM and the Descending Factor Check Method for determining GCF are two complementary methods that make up the simplified enumeration strategy presented in this study. The suggested approaches prioritize logical starting points, directional checking, and early termination once conditions are met rather than depending on exhaustive listings or prime factorization. The enumeration process is physically and visually represented using a gear-based instructional model, which improves conceptual comprehension. According to the results, these tactics are especially useful for young and inexperienced learners because they encourage effectiveness, simplicity, and logical reasoning.