Greatest Common Factor (GCF)
The largest number that divides evenly into every number in the list Example: GCF(12, 18) = 6, since 6 is the biggest number both divide into evenly GCF is also called GCD (greatest common divisor) or HCF (highest common factor) — same calculation, different names depending on the textbook. It's most commonly used to simplify a fraction to its lowest terms, since dividing both the numerator and denominator by their GCF is exactly what "simplifying" means.
Least Common Multiple (LCM)
The smallest number that every number in the list divides into evenly Example: LCM(12, 18) = 36, since 36 is the smallest number both divide into evenly LCM shows up most often when adding or subtracting fractions with different denominators — the least common multiple of the denominators is the smallest common denominator that lets both fractions be rewritten with matching bottoms. It's also useful for scheduling problems: if one event repeats every 12 days and another every 18, they next coincide on day 36.
How GCF and LCM relate
For any two numbers, their GCF and LCM are connected: GCF × LCM equals the product of the two numbers themselves. For 12 and 18: GCF is 6, LCM is 36, and 6 × 36 = 216 = 12 × 18. This relationship is exactly how LCM is calculated once GCF is known, without needing to list out multiples by hand.
Frequently asked questions
What is the GCF of 12 and 18?
6. It's the largest number that divides evenly into both 12 and 18 (12 ÷ 6 = 2, 18 ÷ 6 = 3, both whole numbers).
What is the LCM of 12 and 18?
36. It's the smallest number that both 12 and 18 divide into evenly (36 ÷ 12 = 3, 36 ÷ 18 = 2, both whole numbers).
Is GCF the same as GCD?
Yes. GCF (greatest common factor), GCD (greatest common divisor), and HCF (highest common factor) all refer to the identical calculation — just different names used in different textbooks and regions.
Can you find the GCF and LCM of more than two numbers?
Yes — enter as many numbers as needed, separated by commas, spaces, or new lines. GCF(12, 18, 24) is 6, and LCM(12, 18, 24) is 72.