A free original bilingual lesson on HCF and LCM of two or three positive integers. Use prime powers to explain each calculation, distinguish a common divisor from a common multiple, and model largest equal groups and the next common event under explicit conditions. Verify the product identity for two positive integers and reduce a specified-remainder problem to exact divisibility. The lesson includes worked examples, an analogy, a quick reference and 12 practice questions with full explanations. It is one foundation topic within Numbers and Calculation, not a complete Mathematics course or full CBT simulation.