Common Multiple Calculator — LCM & Multiples List
Enter two positive integers to find their least common multiple (LCM) — the smallest number divisible by both — and list as many common multiples as you need. The LCM is also used to find the common denominator when adding fractions.
Smallest positive integer that is divisible by both numbers
- 1
GCF (Euclidean algorithm)
2Computed by repeatedly replacing (a, b) with (b, a mod b) until b = 0. - 2
LCM = a × b ÷ GCF
4 × 6 ÷ 2 = 12
How does this calculator work?
LCM(a, b) = a × b ÷ GCF(a, b), where GCF is found by the Euclidean algorithm. Every common multiple is a whole-number multiple of the LCM: k × LCM. Enter two integers and a count to get the LCM and a list of common multiples.
Formula
How this is calculated
The least common multiple of two integers is the smallest positive integer into which both divide evenly. It can be computed from the greatest common factor (GCF) using the identity LCM(a, b) = a × b ÷ GCF(a, b). The GCF is found efficiently with the Euclidean algorithm: repeatedly replace the pair (a, b) with (b, a mod b) until b is zero; the last non-zero a is the GCF.
Every common multiple of a and b is a positive integer multiple of the LCM. So the kth common multiple is simply k × LCM(a, b). For example, LCM(4, 6) = 12, and the common multiples are 12, 24, 36, 48, … The sequence grows linearly with k.
The LCM has direct applications in arithmetic: the least common denominator (LCD) when adding fractions equals the LCM of their denominators. It also appears in scheduling (when two events next coincide), gear-ratio analysis, and the Chinese Remainder Theorem in number theory.
Frequently asked questions
They are related by LCM(a, b) × GCF(a, b) = a × b. So if you know one, you can find the other without separate computation. This identity also shows that coprime numbers (GCF = 1) always have LCM = a × b.
To add fractions with different denominators, you need the least common denominator (LCD), which equals the LCM of the denominators. For example, to add 1/4 + 1/6: LCM(4, 6) = 12, so rewrite as 3/12 + 2/12 = 5/12.
Yes — apply the formula pairwise: LCM(a, b, c) = LCM(LCM(a, b), c). Each step reduces the problem to two numbers until all are included. For example, LCM(4, 6, 9) = LCM(12, 9) = 36.
Also known as
TG we-Calculate Editorial Team. (2026). Common Multiple Calculator — LCM & Multiples List [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/common-multiple-calculator
TG we-Calculate Editorial Team. "Common Multiple Calculator — LCM & Multiples List." TG we-Calculate. 2026. https://we-calculate.com/calculator/common-multiple-calculator.
TG we-Calculate Editorial Team, "Common Multiple Calculator — LCM & Multiples List," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/common-multiple-calculator
@misc{wecalculate_common_multiple_calculator, title = {Common Multiple Calculator — LCM & Multiples List}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/common-multiple-calculator}}, year = {2026}, note = {TG we-Calculate} }
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