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Number Theory Calculators

LCM Calculator

Find the least common multiple (LCM) of two or more whole numbers, with prime factorisations and steps.

Enter values

Separate values with commas, spaces or new lines.

Results update as you type.

Result

LCM

180

Step-by-stepShow
  1. 12 = 2^2 × 3
  2. 18 = 2 × 3^2
  3. 30 = 2 × 3 × 5
  4. LCM = product of the highest power of each prime

About the LCM Calculator

Find the least common multiple (LCM) of two or more whole numbers, with prime factorisations and steps.

Also known as: least common multiple, lowest common multiple, lcm of numbers, lcd calculator, least common denominator.

How to use this calculator

  1. Enter whole numbers.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Open “Step-by-step” to see how the answer was worked out.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

LCM(a, b) = |a × b| ÷ GCD(a, b)

Worked example

Using the values pre-filled in the calculator above:

  • Whole numbers: 12, 18, 30

the calculator returns:

  • LCM: 180

Working

  1. 12 = 2^2 × 3
  2. 18 = 2 × 3^2
  3. 30 = 2 × 3 × 5
  4. LCM = product of the highest power of each prime

Frequently asked questions

What is the LCM used for?

The LCM is the smallest number that all given numbers divide into. It is used to find common denominators when adding fractions and to solve scheduling problems (when will two cycles line up again).