LCM Calculator

Find the smallest positive number divisible by every integer in your list. Compare the prime powers and see how each number fits into the common multiple.

2–100 non-zero integers, each at most 10¹² in magnitude. Negative signs are ignored; decimals and invalid tokens are rejected.

Least common multiple

180

LCM(12, 18, 30) = 180 · GCF = 6

  • 12 =2^2 × 3
  • 18 =2 × 3^2
  • 30 =2 × 3 × 5
  • Highest power of each prime2^2 × 3^2 × 5
  • LCM180
  • 180 ÷ 1215
  • 180 ÷ 1810
  • 180 ÷ 306

How this was calculated

Factor each number into primes, take every prime at its highest power, and multiply: 2^2 × 3^2 × 5 = 180.

How to find the least common multiple

Factor each input into primes. For each prime appearing anywhere in the list, keep its highest exponent; multiply those prime powers. This produces the smallest positive number divisible by all the inputs.

For two positive integers, LCM(a, b) = (a ÷ GCF(a, b)) × b. Apply that operation repeatedly for a longer list. The calculator checks safe integer precision rather than presenting a rounded large integer as exact.

Example: 12, 18 and 30

12 = 2² × 3, 18 = 2 × 3², and 30 = 2 × 3 × 5. Keeping the highest powers gives 2² × 3² × 5 = 180. Check the result: 180 ÷ 12 = 15, 180 ÷ 18 = 10, and 180 ÷ 30 = 6.

Common denominators and repeating events

An LCM supplies a common denominator when adding fractions. For events repeating every 12 and 18 days from the same starting point, the first shared repeat is after 36 days. If starting times differ, the LCM alone does not determine the next coincidence.

Enter 2–100 non-zero integers with magnitudes at most 10¹². Negative signs are ignored. Zero is excluded because this tool seeks a positive common multiple. Decimal or invalid entries cause the whole list to be rejected.

Frequently asked questions

Is LCM the same as GCF?

No. The LCM is a multiple of every input; the GCF divides every input. For 12 and 18, the LCM is 36 and the GCF is 6.

Why can a large LCM be rejected?

Even small inputs can produce a very large LCM. This tool rejects an LCM above 9,007,199,254,740,991, the largest safely represented integer in its number calculations.

Last updated . Results are estimates for informational purposes only.