GCF & LCM Calculator
Find the Greatest Common Factor (GCF/HCF/GCD) and Least Common Multiple (LCM) for any group of numbers, with prime factorization steps.
GCF = largest number dividing all inputs (use for simplifying fractions). LCM = smallest number divisible by all inputs (use for adding fractions). Key relationship: GCF × LCM = a × b (for two numbers).
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GCF/LCM Terminology by Country
| Country | GCF name | LCM name | Local term |
|---|---|---|---|
| 🇺🇸 USA | GCF | LCM | Greatest Common Factor |
| 🇬🇧 UK | HCF | LCM | Highest Common Factor |
| 🇩🇪 Germany | ggT | kgV | größter gemeinsamer Teiler / kleinstes gemeinsames Vielfaches |
| 🇫🇷 France | PGCD | PPCM | Plus grand commun diviseur / Plus petit commun multiple |
| 🇯🇵 Japan | 最大公約数 | 最小公倍数 | Saidai Kouyakusuu / Saishou Koubaisuu |
| 🇮🇳 India | HCF | LCM | Highest Common Factor |
| 🇪🇸 Spain | MCD | MCM | Máximo común divisor / Mínimo común múltiplo |
Frequently Asked Questions
How do you find the GCF using prime factorization?
Factor each number into primes. GCF = product of common prime factors at their lowest power. Example: 12 = 2²×3, 18 = 2×3². Common factors: 2¹ and 3¹. GCF = 2×3 = 6.
How do you find the LCM using prime factorization?
Factor each number. LCM = product of all prime factors at their highest power. Example: 12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 4×9 = 36.
What is Euclid's algorithm for GCF?
GCF(a,b) = GCF(b, a mod b), where 'mod' is the remainder. Repeat until remainder = 0. Example: GCF(48, 18): GCF(48,18) → GCF(18,12) → GCF(12,6) → GCF(6,0) = 6. Very efficient for large numbers.
When do you use LCM vs GCF?
Use GCF to simplify fractions (divide top and bottom by GCF). Use LCM to add fractions with different denominators (the common denominator is the LCM). Example: 1/4 + 1/6 → LCM(4,6)=12 → 3/12 + 2/12 = 5/12.