FinanceCalcs
GCF and LCM Calculator
Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of any two or three numbers — with full step-by-step working shown using prime factorization. Essential for simplifying fractions and adding fractions with different denominators.
Prime Factorization
How We Got There
"GCF tells you the largest number that divides evenly into both. LCM tells you the smallest number that both divide into evenly. You need both when working with fractions!"
GCF vs LCM — what’s the difference?
The GCF (Greatest Common Factor) is the biggest number that divides evenly into all your numbers. It’s used to simplify fractions. For example, to simplify 12/18, find GCF(12,18) = 6, then divide top and bottom by 6 to get 2/3.
The LCM (Least Common Multiple) is the smallest number that all your numbers divide into evenly. It’s used to add or subtract fractions with different denominators. To add 1/4 + 1/6, find LCM(4,6) = 12, then convert both fractions to 12ths: 3/12 + 2/12 = 5/12.
Quick Questions
What is prime factorization?
Prime factorization means writing a number as a product of its prime factors. For example, 12 = 2 × 2 × 3, and 18 = 2 × 3 × 3. Every number has a unique prime factorization — it’s like a “fingerprint” for that number.
GCF is also called HCF — same thing?
Yes! GCF (Greatest Common Factor) and HCF (Highest Common Factor) are exactly the same thing. GCF is more common in the US, HCF is more common in the UK and Australia. Some textbooks also call it GCD (Greatest Common Divisor).
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