Least Common Multiple Calculator
Find the smallest shared multiple of two or more integers — common denominators, repeating schedules, gear teeth — not the greatest shared factor.
How to use
- Paste at least two whole numbers, separated by spaces, commas or new lines.
- Read the least common multiple. lcm(12, 18) is 36; lcm(4, 6, 8) is 24.
- Ignore minus signs: lcm(−12, 18) is still 36.
- Use GCF when you want the largest shared divisor, or Factor to list one number’s factors.
How it works
The least common multiple is the smallest positive integer that every input divides. 12 and 18 both divide 36, and nothing smaller positive works. The identity is |a×b| ÷ gcd(a,b): 216 ÷ 6 = 36.
A longer list folds left to right: lcm(4, 6) = 12, then lcm(12, 8) = 24. That is why 4, 6 and 8 share 24, not 48.
Adding a 0 forces LCM 0 under this definition. Decimals are rejected — LCM is an integer idea. Overflow past safe integers is withheld rather than silently rounded.
Classroom uses: the first time two repeating events coincide (every 4 days and every 6 days: day 12), or a common denominator for 1/4 + 1/6 (12). GCF answers a different question (largest shared piece). Confusing them is how 12 and 18 become 6 when you wanted 36.
Coprime inputs make LCM the product: lcm(5, 7) = 35. A third number can jump past that product: lcm(5, 7, 10) = 70. Bus or bell schedules that skip weekends still need a calendar tool; LCM only aligns integer day counts.
Formula
lcm(a, b) = |a × b| ÷ gcd(a, b) lcm(12, 18) = 216 ÷ 6 = 36
Worked examples
Two numbers
12 and 18 → 36
Three numbers
4, 6, 8 → 24
Shared multiples people expect
| Numbers | LCM |
|---|---|
| 12, 18 | 36 |
| 4, 6, 8 | 24 |
| 5, 7 | 35 |
| 4, 6 | 12 |
| 8, 15 | 120 |
| 5, 7, 10 | 70 |
Useful notes
- LCM is a multiple; GCF is a factor. They are inverses via the product identity.
- Decimals are rejected.
- A 0 in the list makes the LCM 0.
FAQ
- How do I find the LCM of two numbers?
Divide the absolute product by the greatest common factor. 12 and 18 share a GCF of 6, so LCM = 216 ÷ 6 = 36.
- Can I enter more than two numbers?
Yes. The LCM of a list is built pairwise. 4, 6 and 8 share 24.
- What is the LCM of a number and 0?
0. The only common multiple of n and 0 that this definition keeps is 0.
- What is lcm(5, 7) when the numbers are coprime?
35 — the product, because gcd(5, 7) = 1.
- When do I want GCF instead?
When you are simplifying a fraction or a ratio, or splitting something into the largest equal piles. LCM is for aligning cycles and denominators.
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