What this calculator does
A common multiple of a set of numbers is any number that all of them divide into evenly. The smallest of these is the lowest common multiple, or LCM, but there are infinitely many others above it: the LCM itself, then twice the LCM, three times the LCM, and so on. This calculator lists as many of those as you ask for.
This is useful whenever a single "smallest" answer is not quite what is needed, such as finding several dates, cycle lengths, or repeat intervals that line up, rather than just the very first one.
The formula
The lowest common multiple of the numbers entered is found first using the standard greatest-common-divisor method. Every other common multiple of that set is then simply a whole-number multiple of the LCM, so the list is built by multiplying the LCM by 1, 2, 3, and so on up to the count requested.
| Term | Meaning |
|---|---|
| Common multiple | A number that every value in the set divides into with no remainder. |
| Lowest common multiple (LCM) | The smallest positive common multiple of the set; every other common multiple is a whole-number multiple of it. |
| Multiple index | Which position a listed multiple occupies: the 1st common multiple is the LCM itself, the 2nd is twice the LCM, and so on. |
The inputs explained
| Field | What to enter |
|---|---|
| Numbers (comma separated) | The numbers to find common multiples for, separated by commas. |
| How many multiples to list | How many common multiples to list, starting from the smallest. |
When to use it
Lining up repeating schedules
If one event repeats every 4 days and another every 6 days, listing several common multiples shows every day in the near future when both line up, not just the first one.
Classroom maths practice
Seeing a run of common multiples laid out side by side makes the underlying pattern, and the relationship to the LCM, more concrete than a single answer.
Checking a pattern by hand
Comparing a hand-worked list of common multiples against the calculator’s output is a quick way to catch an arithmetic slip.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Common multiples of 4 and 6, by how many are listed
The same pair of numbers with a growing count of multiples requested.
| Count requested | Lowest common multiple | First common multiples |
|---|---|---|
| 3 | 12 | 12, 24, 36 |
| 5 | 12 | 12, 24, 36, 48, 60 |
| 8 | 12 | 12, 24, 36, 48, 60, 72, 84, 96 |
| 10 | 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 |
| 15 | 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180 |
| 20 | 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240 |
Questions
How is this different from a GCD & LCM calculator?
The GCD & LCM calculator gives the single smallest common multiple. This calculator builds on that by listing several common multiples in sequence, for when more than just the smallest is needed.
Is every common multiple a multiple of the LCM?
Yes. That is a defining property: once the LCM is known, every other common multiple of the set is simply the LCM multiplied by a whole number.
What happens if I enter only one number?
With a single number, its common multiples are just its own multiples, since there is nothing else to share a common multiple with.
Is there a limit to how many multiples I can list?
The calculator accepts a count of up to 200, which comfortably covers any practical use without producing an unmanageable list.
For just the lowest common multiple and the greatest common divisor of a set, see the GCD & LCM calculator.