Two integers
For 18 and 24, the GCF is 6 and the LCM is |18 × 24| / 6 = 72.
Compare factors and multiples
GCF and LCM calculator
Find the greatest common factor and least common multiple for a list of integers, then see how each result is built.
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Formula and steps included
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Formula
GCF and LCM definitions and formula
GCF(a, b) = greatest positive integer dividing both; LCM(a, b) = |a × b| / GCF(a, b) for nonzero integers
The greatest common factor is the largest positive integer that divides every value without a remainder. It is useful for reducing fractions and dividing quantities into equal groups.
The least common multiple is the smallest positive multiple shared by every nonzero value. For more than two integers, compute the GCF or LCM one pair at a time.
How to use the formula
Use integer values
Work with absolute values for factors and multiples; a negative sign does not change the positive GCF or LCM.
Find the GCF
List common factors, compare prime factorizations, or repeatedly use the Euclidean algorithm.
Find the LCM
For two nonzero integers, divide the absolute product by their GCF.
Extend across the list
Combine the first two values, then combine that result with each remaining value in turn.
Worked examples
GCF and LCM calculator examples
Three integers
For 8, 12, and 20, the GCF is 4 and the LCM is 120.
Common questions
GCF and LCM calculator FAQ
When should I use GCF instead of LCM?
Use GCF to split quantities into the largest equal groups or simplify a fraction. Use LCM to find the first shared cycle, common denominator, or matching interval.
What happens when one of the numbers is zero?
The GCF of zero and a nonzero integer is the absolute value of that integer. An LCM involving zero is conventionally zero because zero is a multiple of every integer.
Do negative integers change the GCF or LCM?
No. GCF and LCM are reported as nonnegative values, so calculations use the integers' absolute values.
Does the tool save my list of integers?
Your integer list is not saved by default or uploaded. You can opt into Remember on this device or download a local JSON backup.