justyourcalculatorLeast Common Multiple Calculator
Find the least common multiple of any set of numbers, with steps.
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LCM Calculator
Least common multiple of a set of numbers
Separate with commas or spaces.
LCM(12, 18, 30)
180
- Next common multiples
- 360, 540, 720
How it was calculated
- 12 = 2² × 3
- 18 = 2 × 3²
- 30 = 2 × 3 × 5
- Take each prime at its highest power: 2² × 3² × 5
- LCM = 2² × 3² × 5 = 180
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How the lcm calculator works
The least common multiple is the smallest positive number that every number in the set divides into evenly. It's what you need to add fractions with different denominators (the least common denominator).
Prime factorization method: factor each number, then multiply every prime that appears, using its highest power. For 12 = 2² × 3, 18 = 2 × 3² and 30 = 2 × 3 × 5, the LCM is 2² × 3² × 5 = 180. For two numbers there's a shortcut: LCM(a, b) = a × b / GCF(a, b).
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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