About the LCM calculator
The least common multiple (LCM) is the smallest positive number that every number in your list divides into evenly. This calculator finds the LCM of two or more whole numbers, shows the greatest common factor alongside, and displays prime factorisations for context.
It is useful for adding fractions with different denominators and for scheduling repeating events.
Who should use the LCM calculator
- Students working with fractions and number theory.
- Teachers wanting quick checks.
- Anyone finding when repeating cycles line up.
How to use the LCM calculator: what each input means
- Numbers
- Two or more whole numbers, separated by commas, spaces or new lines. Negative signs are ignored.
How the LCM calculator works: method and formula
For two numbers, LCM(a, b) = a × b ÷ GCF(a, b). For more numbers the calculation is repeated, combining the running result with each next number. The calculator uses exact big-integer arithmetic, so there is no overflow.
- Two numbers
- LCM(a, b) = |a × b| ÷ GCF(a, b)
How to read your LCM calculator result
The LCM is always at least as large as the largest number. If the numbers share no common factor other than 1 (they are coprime), the LCM equals their product.
LCM Calculator worked example
Find the LCM of 21, 14 and 38.
- 21 = 3 × 7, 14 = 2 × 7 and 38 = 2 × 19.
- Take each prime at its highest power: 2, 3, 7 and 19.
- LCM = 2 × 3 × 7 × 19 = 798.
LCM(21, 14, 38) = 798.
Practical uses of the LCM calculator
- Finding a common denominator for fractions.
- Working out when two repeating schedules coincide.
- Solving gear and rhythm problems.
Assumptions and limitations of this calculator
- Whole numbers only. Input is limited to 100 numbers of up to 150 digits each.
- If any number is zero, the LCM is reported as 0.