Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.
GCF and LCM Calculator
LiveGreatest Common Factor (GCF)
12
Least Common Multiple (LCM)
72
Works with two or more positive whole numbers.
The concepts
GCF: the largest number that divides evenly into all the given numbers
LCM: the smallest number that all the given numbers divide evenly into
Example
24 and 36: GCF = 12 (both divide evenly by 12, and no larger number works), LCM = 72 (the smallest number both 24 and 36 divide into evenly).
Step-by-step guide
- Enter two or more whole numbers, separated by commas.
- Read the GCF and LCM.
Common mistakes
Confusing GCF with LCM - GCF is always less than or equal to the smallest number given; LCM is always greater than or equal to the largest.
Using decimals or negative numbers - GCF and LCM are defined for positive whole numbers.
Frequently asked questions
Where is GCF used?
GCF is commonly used to simplify fractions - dividing both the numerator and denominator by their GCF reduces a fraction to its lowest terms.
Where is LCM used?
LCM is used to find a common denominator when adding or subtracting fractions with different denominators, and in scheduling problems (like when two repeating events next line up).
What if the numbers share no common factor besides 1?
Then the GCF is 1, and the numbers are called "coprime." In that case, the LCM is simply the product of the numbers.
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