Sumivo · Mathematics
LCM Calculator
Find the least common multiple of two or more integers — the smallest positive number they all divide into.
01 / inputs
integers
02 / result
LEAST COMMON MULTIPLE
24
- LCM
- 24
- GCD
- 2
- Count
- 3
Calculation trace
- lcm(4, 6) = 4 × 6 ÷ gcd(2) = 1212LCM step 1
- lcm(12, 8) = 12 × 8 ÷ gcd(4) = 2424LCM step 2
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How it works
The least common multiple (LCM) is the smallest positive integer that every input divides into with no remainder. The tool folds the list two at a time using lcm(a, b) = |a × b| ÷ gcd(a, b), where the greatest common divisor gcd(a, b) is found with the Euclidean algorithm; for three or more numbers, lcm(a, b, c) = lcm(lcm(a, b), c).
Assumptions & limits
- Inputs must be non-zero integers; decimals and zero are rejected.
- A negative sign is ignored — a number and its negation have the same LCM.
- Results above 2^53 may lose exact integer precision, and a warning is shown.
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FAQ
- What is the least common multiple?
- The smallest positive integer that each of your numbers divides into evenly. For 4 and 6 the LCM is 12.
- How is the LCM related to the GCD?
- They satisfy lcm(a, b) × gcd(a, b) = |a × b|, so the LCM equals the product of two numbers divided by their greatest common divisor.
- Why can’t the LCM include zero?
- Zero has no positive multiples in common with other numbers, so the least common multiple involving 0 is undefined.
- What is the LCM used for?
- Adding or comparing fractions with different denominators, finding when repeating events line up again, and gear or timing problems all rely on the LCM.
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Related calculators
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SOURCES
- OpenStax, Rice UniversityPrealgebra 2e ↗
Least common multiple: listing multiples and prime factorization
Accessed 2026-09-02