Least Common Multiple (LCM) Calculator
Greatest common factor and least common multiple of 2–10 numbers, with the Euclidean algorithm shown step by step and the prime factorization of every number.
Processed entirely in your browser — nothing you enter here is ever uploaded.
Result
About this tool
This page opens the calculator with the least common multiple highlighted as the main result: paste 2 to 10 whole numbers and run it to get the smallest number they all divide into. The LCM is derived through the identity lcm(a, b) = a × b ÷ gcd(a, b), so for 48 and 180 you see 48 × 180 ÷ 12 = 720 with the gcd steps right above.
For longer lists the calculator folds the identity pairwise — lcm(a, b, c) = lcm(lcm(a, b), c) — and because all arithmetic uses exact big integers, the LCM of many large numbers is computed without the overflow that breaks ordinary calculators. The prime factorization of each input shows why the LCM takes the highest power of every prime involved.
The LCM is the number behind common denominators when adding fractions, repeating schedules that need to line up (buses every 48 and 180 minutes meet every 720), gear rotations and countdown cycles. The greatest common factor is computed in the same run for free.
Example. The integers 12 and 18 produce a greatest common factor of 6 and a least common multiple of 36.
Limit. The input must be 2 to 10 integers, each with at most 12 digits, because factorization is trial division.