Greatest Common Factor (GCF) & Least Common Multiple (LCM) Practice Problems
Master finding the Greatest Common Factor (GCF/HCF) and Least Common Multiple (LCM) using prime factorization trees, Venn diagrams, and Euclidean division algorithms.
🧠 Core Problem-Solving Strategies
🌳 Prime Factorization Venn Diagram
Break numbers into prime factors: GCF is the product of SHARED prime factors; LCM is the product of ALL unique prime factors with highest powers.
⚡ GCF × LCM = a × b Product Invariant
For any two positive integers a and b, the product of their GCF and LCM is always equal to a × b: LCM(a,b) = (a × b) / GCF(a,b).
🪜 Stepwise Factor Listing for Benchmark Pairs
For small numbers like 12 and 18, list common factors (1, 2, 3, 6) ➔ GCF = 6; and multiples (12, 24, 36...) ➔ LCM = 36.
❓ Frequently Asked Questions
What is the difference between a factor and a multiple?
A factor divides evenly into a number (smaller or equal). A multiple is the result of multiplying the number by an integer (larger or equal).
How do you find the LCM of 3 numbers?
Write the prime factorizations of all 3 numbers, and take the highest power of each prime that appears in any of the factorizations.
Continue Learning & Practicing
Reinforce your understanding with printable worksheets, step-by-step guides, calculators, and speed games: