HCF-LCM Relationship

For exactly TWO numbers a and b, HCF(a,b) × LCM(a,b) = a × b. This single identity is a CAT favourite because it lets you find any one of the four quantities from the other three: a missing LCM is (a×b)/HCF, and a missing number is (HCF×LCM)/a. A crucial warning — the identity holds only for two numbers; for three or more it fails, so never write HCF×LCM = product of three numbers. Two linked facts make the topic richer: the HCF always divides the LCM, and if two numbers are written as HCF×m and HCF×n then m and n must be coprime (their own HCF is 1), with LCM = HCF×m×n. CAT often gives the HCF, the LCM and one number and asks for the other, or gives the product and HCF and asks for the LCM.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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