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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.

Processing... 0%
Parsing numbers
Running the Euclidean algorithm
Factoring into primes
Done

Result

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.

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Accepted Formats & Rules

  • GCF and LCM of 2 to 10 whole numbers in one run.
  • Step-by-step Euclidean algorithm and the lcm(a, b) = a × b ÷ gcd(a, b) working shown.
  • Prime factorization of every number in exponent form (48 = 2⁴ × 3).

Key Benefits

✓ Shows every division of the Euclidean algorithm, so the GCF is not just an answer but a worked example.
✓ Exact big-integer arithmetic: the LCM of many large numbers is computed without overflow or rounding.
✓ Prime factorization of each input in exponent form makes the shared and missing factors obvious.

Use Cases

  • • Find the GCF of 48 and 180 with every Euclidean division written out, to reduce a fraction or check math homework.
  • • Compute the LCM of several numbers to find a common denominator or the moment repeating schedules line up again.
  • • See the prime factorization of each number in exponent form (48 = 2^4 × 3) to understand which factors are shared.