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Least Common Multiple Calculator

The least common multiple (LCM) is the smallest number that is a multiple of every number in a list. It is essential for adding fractions with different denominators and for scheduling repeating events.

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LCM Calculator

Least Common Multiple Finder

About the Least Common Multiple Calculator

The least common multiple (LCM) is the smallest number that is a multiple of every number in a list. It is essential for adding fractions with different denominators and for scheduling repeating events.

How to use the Least Common Multiple Calculator

  1. Enter your numbers separated by spaces or commas.
  2. Press Find Least Common Multiple.

Formula and method

lcm(a, b) = |a × b| ÷ gcd(a, b). For more than two numbers, apply it repeatedly.

Worked example

For 12, 15 and 20: lcm(12, 15) = 60 and lcm(60, 20) = 60.

Repeating events. If one bus comes every 4 minutes and another every 6 minutes, they arrive together every LCM(4, 6) = 12 minutes.

When to use the Least Common Multiple Calculator

  • Finding a common denominator when adding fractions.
  • Working out when two repeating events will happen together.
  • Solving scheduling and timing problems.

Common mistakes to avoid

  • Confusing the LCM with the GCF.
  • Simply multiplying the numbers. That gives a common multiple, but not always the lowest.

Tips

  • Use the LCM as the common denominator when adding fractions.
  • For coprime numbers the LCM is simply their product.

Frequently asked questions

How is the LCM used in real life?
To find when repeating events line up, for example two buses that leave every 12 and 15 minutes meet again after 60 minutes.
What is the relationship between LCM and GCF?
For two numbers, LCM × GCF equals the product of the numbers.
Can the LCM be found for more than two numbers?
Yes. Find the LCM of the first two, then the LCM of that result with the next number.