Applied Number Theory: Calculating GCF & LCM to Solve Real-World Problems
The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are indispensable mathematical tools. When we need to partition or divide items into equal groups of the largest possible size, we compute the GCF. When we need to determine when recurring cyclic events will occur simultaneously in the future, we compute the LCM. In this lesson, students learn how to determine both GCF and LCM accurately using prime factor decomposition and Venn diagrams.
📊 GCF vs LCM for Numbers 12 and 18
Prime factorization of 12: 2 × 2 × 3
Prime factorization of 18: 2 × 3 × 3
2 × 3 = 6
2 × 3 × 2 × 3 = 36
A school has 20 red pens and 30 blue pens. What is the greatest number of identical bags they can pack with equal numbers of pens?
Solution: We need to find the GCF of 20 and 30: GCF(20, 30) = 10 bags.
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