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Least Common Multiple Calculator

Enter two or more numbers separated by commas to find their least common multiple (LCM), greatest common factor (GCF) and prime factorization.

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Least Common Multiple (LCM) Calculator

LCM & Factorization Result

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Definition: Smallest common multiple
Formula: LCM(a,b) = |a·b| / GCF(a,b)
Inputs: Two or more numbers
Use case: Common denominators, scheduling

What is the least common multiple?

The least common multiple of a set of numbers is the smallest positive number that is a multiple of every number in the set. For 4 and 6, the multiples of 4 are 4, 8, 12, 16... and the multiples of 6 are 6, 12, 18... so the LCM is 12.

The fastest way to compute it is LCM(a, b) = |a × b| / GCF(a, b). For more than two numbers, apply the formula repeatedly. The calculator does this automatically and reports the result for any list you enter.

Why the LCM matters

The LCM gives the common denominator when adding or subtracting fractions, which is why fraction calculators rely on it. It also solves scheduling problems: two buses that arrive every 6 and 8 minutes both arrive at the station together every 24 minutes.

Prime factorization shows how the LCM is built: take each prime factor to the highest power that appears in any number. The calculator displays these factorizations for every input.

How to use this calculator

  1. Type the numbers separated by commas, for example 12, 18, 24.
  2. Press Calculate LCM.
  3. Read the LCM and GCF of the whole list.
  4. Check the prime factorization of each number to see why.

Pro tips

  • Use the LCM as a common denominator when adding fractions by hand.
  • The LCM of two co-prime numbers is always their product.
  • Order does not matter — the LCM is the same for any arrangement of the list.

Advantages & considerations

✅ Advantages

  • Works with two or more numbers
  • Shows GCF and prime factorizations
  • Instant results for common-denominator problems

⚠️ Considerations

  • Only accepts positive integers
  • Very large lists are best kept under a dozen numbers

Frequently asked questions

What is the LCM of 4 and 6?▶
12. It is the smallest number divisible by both: multiples of 4 are 4, 8, 12... and multiples of 6 are 6, 12, 18... so the first common multiple is 12.
How is LCM calculated?▶
Using LCM(a,b) = |a × b| / GCF(a,b). For more numbers, apply the formula repeatedly, or use prime factors raised to their highest powers.
What is LCM used for?▶
It finds common denominators for fractions and solves periodic scheduling problems where events repeat at different intervals.
What is the LCM of two prime numbers?▶
Since primes share no factors, their LCM is simply their product. For example LCM(3, 5) = 15.
What is the difference between LCM and GCF?▶
The LCM is the smallest shared multiple; the GCF is the largest shared divisor. They are related by LCM(a,b) × GCF(a,b) = a × b.