A little clarity, calculated.

culators
EN

Math / Least Common Multiple

Least Common Multiple Calculator

Find the least common multiple of two positive integers, the smallest positive number divisible by both. The result is useful for aligning repeating cycles and finding a common denominator for whole-number fractions. For positive integers a and b, lcm(a,b)=a×b/gcd(a,b). Euclid’s algorithm finds the greatest common divisor efficiently.

Your inputs

Make it your own
Calculator settings

Your result
36
Least common multiple

Example inputs shown. Adjust them to explore.

A familiar situation

Find when two repeating schedules next line up by calculating their least common multiple.

How to use this calculator

  1. Enter first integer, second integer.
  2. Select Calculate to see the answer and its breakdown.
  3. Keep a scenario, change an input and compare the results.

Use consistent units and check the assumptions below before applying the result.

How least common multiple is calculated

For positive integers a and b, lcm(a,b)=a×b/gcd(a,b). Euclid’s algorithm finds the greatest common divisor efficiently. The least common multiple of 12 and 18 is 36, the first positive multiple shared by both.

lcm(a,b)=|a×b|/gcd(a,b).
A worked example

The least common multiple of 12 and 18 is 36, the first positive multiple shared by both.

Assumptions & useful context

The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.

Frequently asked questions

Can negative integers be entered?

The calculator accepts nonzero integers and uses their absolute values.

What is the LCM of identical integers?

Their absolute value.

Find a calculator