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LCM Calculator

Find the least common multiple (LCM) of two or more whole numbers, with the prime factorization method and the GCF.

Results

ItemValue

Steps

StepWorking
Enter 2 to 10 whole numbers from 1 to 1,000,000. The LCM is shown exactly, even when it is very large.

Quick Answer

The least common multiple (LCM) is the smallest number that every number in a list divides into evenly. For 12, 18 and 30, the LCM is 180. One way to find it: write each number as prime factors, then multiply the highest power of each prime: 2² × 3² × 5 = 180.

Last updated: 2 November 2026 ·How we calculate this: prime factorization method

Table of Contents

How This LCM Calculator Works

Type two or more whole numbers. The calculator breaks each one into prime factors, takes the highest power of every prime that appears, and multiplies them together. It also shows the greatest common factor (GCF) for comparison.

Quick explanation: LCM = product of the highest power of each prime in any of the numbers.

  • Up to 10 numbers: separate them with commas or spaces.
  • Prime factors: shown for each number in the steps.
  • GCF: the largest number that divides all of them.

How to Use the LCM Calculator

  1. Type two or more whole numbers, separated by commas or spaces.
  2. Press Calculate.
  3. Read the LCM and the GCF.
  4. Check the prime factors of each number in the steps table.
  5. See how the highest powers multiply to give the LCM.

Core Formulas

  • Prime method: LCM = product of each prime at its highest power
  • Two numbers: LCM(a, b) = a × b ÷ GCF(a, b)
  • More numbers: LCM(a, b, c) = LCM(LCM(a, b), c)

Key Terms

  • Multiple: the result of multiplying a number by a whole number, such as 12, 24 and 36 for 12.
  • Common multiple: a number that is a multiple of every number in a list.
  • Prime factor: a prime number that divides a number exactly.
  • Least common denominator: the LCM of the denominators of fractions.

Worked Example

Find the LCM of 8 and 12.

  • 8 = 2³
  • 12 = 2² × 3
  • Highest powers: 2³ and 3
  • LCM = 8 × 3 = 24

Real-Life Examples

  • Hot dogs and buns: hot dogs come in packs of 10 and buns in packs of 8. The LCM is 40, so buy 4 packs of hot dogs and 5 packs of buns to have none left over.
  • Bus timetables: one bus comes every 12 minutes and another every 20. They leave together again after 60 minutes.
  • Adding fractions: for 1/6 + 3/8, the LCM of 6 and 8 is 24, so 4/24 + 9/24 = 13/24.
  • Shift patterns: workers on 4-day and 6-day cycles share a day off every 12 days.

LCM vs GCF

  • LCM: the smallest number that all the numbers divide into. It is at least as big as the largest number.
  • GCF: the largest number that divides all the numbers. It is no bigger than the smallest number.
  • The link: for two numbers, LCM × GCF = a × b.
  • Example: for 8 and 12, the LCM is 24 and the GCF is 4, and 24 × 4 = 96 = 8 × 12.

LCM of Common Pairs

NumbersLCMGCF
2 and 361
4 and 6122
6 and 8242
8 and 12244
9 and 12363
10 and 15305
12 and 18366
15 and 20605
14 and 21427
24 and 367212

When to Use the LCM

  • Adding fractions: the LCM of the denominators is the least common denominator.
  • Schedules: find when two repeating events line up again.
  • Packing: find the smallest amount that fills packs of different sizes exactly.
  • Gears and cycles: find when two turning parts return to the start together.

Common Mistakes to Avoid

  • Multiplying the numbers. 8 × 12 = 96 is a common multiple, but not the least one.
  • Using the lowest prime powers. That gives the GCF. The LCM needs the highest powers.
  • Mixing up LCM and GCF. LCM is a multiple, GCF is a factor.
  • Missing a prime. Include every prime that appears in any of the numbers.
  • Forgetting 1. The LCM of any number and 1 is the number itself.

Frequently Asked Questions

36.

List the prime factors of each number, take the highest power of each prime, and multiply them.

12.

Yes. If one number divides another, the larger is the LCM. The LCM of 4 and 12 is 12.

Their product. The LCM of 5 and 7 is 35.

It gives the least common denominator, which makes adding and subtracting fractions easier.

60.

Write out multiples of each number until you find the first one they share. For 4 and 6: 4, 8, 12 and 6, 12, so the LCM is 12.

No. The LCM is always at least as large as the largest number in the list.

2,520. It is the smallest number that 1, 2, 3 and so on up to 10 all divide into.

Yes: LCM = a × b ÷ GCF. For 8 and 12, that is 96 ÷ 4 = 24.

References & Sources

SourceUsed ForLink
Wikipedia, Least common multiple Methods for finding the LCM. https://en.wikipedia.org/wiki/Least_common_multiple
Wikipedia, Fundamental theorem of arithmetic Prime factorization. https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic