GCD–LCM Relationship

For any two positive integers, GCD and LCM are tied by one clean identity: GCD(a, b) × LCM(a, b) = a × b. This lets you find one from the other without listing anything — if you know a, b and the GCD, then LCM = (a × b)/GCD. It also acts as a sanity check: the GCD must divide the LCM, and both a and b must be multiples of the GCD and factors of the LCM. Note the identity is a two-number rule; it does not extend to three numbers as GCD × LCM = product. A neat consequence the GRE tests: if two numbers are coprime (GCD = 1), their LCM is simply their product. Knowing this relationship converts several "find the other quantity" questions into a single division.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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