Find the least common multiple of two or more numbers.
The LCM is the smallest number that every input divides into. The LCM of 12, 18 and 30 is 180.
The least common multiple (LCM) is the smallest positive number that is a multiple of every number in your list. Enter two or more whole numbers and the calculator shows the LCM, the GCF, how the LCM is built from prime factors and the first eight multiples of the LCM.
LCM is used to add and subtract fractions with different denominators and to find when repeating events coincide. Companion tools: the GCF Calculator, Prime Factorization Calculator and Fraction Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| LCM | 180 |
| GCF | 6 |
| LCM from the prime factors | 2² × 3² × 5 = 180 |
| Prime factors of 12 | 2² × 3 |
| Prime factors of 18 | 2 × 3² |
| Prime factors of 30 | 2 × 3 × 5 |
| Multiple | Value |
|---|---|
| 1 | 180 |
| 2 | 360 |
| 3 | 540 |
| 4 | 720 |
| 5 | 900 |
| 6 | 1,080 |
| 7 | 1,260 |
| 8 | 1,440 |
| Numbers | LCM |
|---|---|
| 4 and 6 | 12 |
| 12, 18, 30 | 180 |
| 7 and 13 | 91 |
| 8, 12, 20 | 120 |
| 15, 25, 35 | 525 |
The smallest positive number that is divisible by all of the given numbers.
Write each number as primes, then multiply each prime to the highest power it appears with.
For two numbers, a × b = LCM × GCF.
Use the LCM of the denominators as the common denominator, then add the numerators.
Their product. The LCM of 7 and 13 is 91.
Scheduling repeating events, gear ratios and aligning cycles — such as buses that arrive every 12 and 18 minutes meeting again after 36 minutes.
It uses the standard method: lcm(a, b) = a × b ÷ gcd(a, b) (prime method: highest power of each prime) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
