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  4. Least Common Multiple Calculator

Least Common Multiple Calculator

Find the LCM of two or more integers with GCD, prime-factorization, and multiples steps.

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How it works

The least common multiple is the smallest positive integer divisible by every input. Methods include listing multiples, max prime powers, and lcm(a, b) = |a · b| / gcd(a, b).

lcm(a, b) = |a · b| / gcd(a, b)

When to use

Use this tool when you need to: try 330, 75, 450, 225 (LCM = 4950) or 21, 14, 38 (LCM = 798). Related: GCF and Factor calculators.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Try 330, 75, 450, 225 (LCM = 4950) or 21, 14, 38 (LCM = 798). Related: GCF and Factor calculators.

Frequently asked questions

What is the Least Common Multiple Calculator?
The least common multiple is the smallest positive integer divisible by every input. Methods include listing multiples, max prime powers, and lcm(a, b) = |a · b| / gcd(a, b).
How do I use the Least Common Multiple Calculator?
Enter the required values, then calculate. The Least Common Multiple Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Least Common Multiple Calculator use?
lcm(a, b) = |a · b| / gcd(a, b)

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Least common multiple

Enter two or more integers separated by commas. The LCM is the smallest positive integer that is divisible by every number you enter.

Separate integers with commas (or spaces). Negative values use absolute magnitude.

Try an example

How it works

What is the least common multiple (LCM)?

In mathematics, the least common multiple — also called the lowest common multiple — of two or more integers is the smallest positive integer that is divisible by each of them. It is commonly written LCM(a, b) or lcm(a, b, …). The LCM appears when you need a shared cycle length (schedules repeating every a and every b days), a common denominator for fractions, or the smallest packing size that fits several unit groups.

Brute force method

The most basic approach lists successive multiples of each integer until a common value appears. Example: find LCM(18, 26) 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234 26: 26, 52, 78, 104, 130, 156, 182, 208, 234 The first shared multiple is 234, so LCM(18, 26) = 234. This is fine for small numbers and tedious for large ones.

Prime factorization method

Factor each integer into primes, then multiply the highest power of every prime that appears in any factorization. Example: LCM(21, 14, 38) 21 = 3 × 7 14 = 2 × 7 38 = 2 × 19 Highest powers: 2 × 3 × 7 × 19 = 798. This is systematic and matches the uniqueness of prime factorizations, though large integers can still be hard to factor by hand.

Greatest common divisor method

For two integers a and b, lcm(a, b) = |a · b| / gcd(a, b) To handle more than two numbers, reduce pairwise: compute q = lcm(a, b), then lcm(q, c), and so on. Example: LCM(21, 14, 38) gcd(14, 38) = 2 → lcm(14, 38) = 14 × 38 / 2 = 266 gcd(266, 21) = 7 → lcm(266, 21) = 266 × 21 / 7 = 798 Order does not matter as long as every number is included. This calculator uses the GCD identity for the official result and also shows the prime-factorization path (and multiples when the numbers are small).

Related calculators

GCF finds the largest shared divisor; the factor and prime tools help inspect the numbers used above.

  • Greatest Common Factor Calculator
  • Factor Calculator
  • Prime Factorization Calculator