The smallest number they all divide into
The least common multiple (LCM) of two or more whole numbers is the smallest positive number that every one of them divides evenly. It is what you need to add or subtract fractions with different denominators and to find when repeating events line up.
This calculator finds the LCM of up to ten numbers, and shows their prime factorisations and the greatest common factor as well.
How it is calculated
Prime-factor each number
Take every prime at its highest power
Multiply them together
For two numbers: LCM × GCF = a × b
Worked example
LCM of 12, 18 and 30
- 12
- 2^2 × 3
- 18
- 2 × 3^2
- 30
- 2 × 3 × 5
- LCM
- 180
Where the LCM is useful
- Adding fractions: 1/12 + 1/18 uses 36 as the common denominator.
- Scheduling: buses that run every 12 and 18 minutes leave together every 36 minutes.
- Gears and tiling problems where repeating patterns must match.
A everyday use
If one bus leaves every 12 minutes and another every 18 minutes, and both just left together, they next leave together after the LCM of 12 and 18 — 36 minutes. The same idea applies to blinking lights, repeating patterns and gear ratios.