How the LCM is calculated
The least common multiple is the smallest positive number that each input divides into evenly. You could list the multiples of every number and look for the first one they share, but that gets tedious quickly.
A faster route uses the greatest common factor: LCM(a, b) equals the absolute value of a × b divided by GCF(a, b). The calculator finds the GCF with the Euclidean algorithm and applies that formula. For three numbers it finds the LCM of the first two, then the LCM of that result with the third.
Reading the result
The main output is the LCM itself, and the supporting value is the GCF used along the way. Together they satisfy the identity GCF × LCM = product of the inputs for two numbers.
For 4 and 6 the GCF is 2 and the LCM is 12, which is the first number both 4 and 6 divide into. The LCM is always at least as large as the biggest input.
Where the LCM is useful
The LCM answers questions about when separate cycles line up.
- Finding a common denominator when adding or subtracting fractions.
- Predicting when repeating events coincide, like two timers or schedules.
- Synchronizing gears, signals, or anything that cycles at fixed intervals.
- Scaling recipes or quantities up to a shared whole-number total.
Common mistakes
Do not mix up the LCM with the GCF. The least common multiple is never smaller than the largest input, whereas the greatest common factor is never larger than the smallest input.
Inputs must be nonzero whole numbers, because zero has no positive multiples that fit the definition. Leave the third field at 0 when you only need the LCM of two numbers.
Formula
lcm(a, b) = |a × b| / gcd(a, b)Frequently asked questions
- Why is the LCM useful?
- It is the common denominator when adding fractions, and it tells you when repeating events line up again.