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Factors, GCF, LCM & Division • Lesson 16 ⏱ 7 min read 📅 Updated Nov 2026

Greatest Common Factor (GCF) and Least Common Multiple (LCM) Explained

Learn the difference between GCF and LCM, how to find them using Prime Factorization and the Euclidean Algorithm, and their real-world uses.

Core Distinction

GCF is about dividing down (simplifying fractions).
LCM is about multiplying up (finding common denominators).

8, 24 9, 18, 36 Overlap: GCF = 12
Venn Diagram: The Overlap Contains Common Factors (Largest is GCF)

Comparison Reference Table

ConceptDefinitionPrimary Math PurposeExample (24 & 36)
GCFLargest number that divides both evenlySimplifying fractions to lowest termsGCF = 12
LCMSmallest number that both divide intoFinding Least Common Denominator (LCD)LCM = 72

The Golden Law: GCF × LCM = a × b

GCF(24, 36) × LCM(24, 36) = 12 × 72 = 864 (24 × 36 = 864)
Try It Yourself

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Solved Step-by-Step Examples:GCF of 12 and 18LCM of 8 and 12GCF of 24 and 36
Your Turn!

Check Your Understanding (3 Quick Questions)

Score: 0 / 3

Question 1: What is the GCF of 24 and 36?

Question 2: What is the LCM of 6 and 8?

Question 3: Which fundamental relation links GCF and LCM for any two numbers a and b?