Greatest Common Factor (GCF/HCF) & Least Common Multiple (LCM)
GCF and LCM are fundamental number theory tools. GCF finds the largest shared divisor to simplify fractions; LCM finds the smallest shared multiple to find common denominators for fraction addition.
๐ง Core Mental Strategies & Shortcuts
โจ GCF Factor Listing Strategy
List all factors of both numbers and circle the largest shared factor: Factors of 20 = [1, 2, 4, 5, 10, 20], Factors of 30 = [1, 2, 3, 5, 6, 10, 15, 30] โ GCF = 10.
๐ LCM Multiple Stride Strategy
Count by the larger number until you hit a multiple of the smaller number: For LCM(4, 6): count by 6s (6, 12) โ 12 is divisible by 4, so LCM = 12.
๐ The Fundamental Product Formula
The product of two numbers always equals their GCF multiplied by their LCM: a ร b = GCF(a, b) ร LCM(a, b).
โ Frequently Asked Questions
What is the difference between a factor and a multiple?
A factor divides into a number with no remainder (factors of 12 are 1, 2, 3, 4, 6, 12). A multiple is produced by multiplying the number (multiples of 12 are 12, 24, 36, 48...). Factors are smaller; multiples are larger.
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