Least Common Multiple (LCM) Calculator

Calculate the least common multiple of two or more numbers instantly. Enter the numbers in the box below to calculate the LCM with step-by-step results. Includes LCM calculation techniques and practical examples.

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LCM =

Step-by-step results:

1. Prime factorization:

2. Select the factors with the highest exponent:

3. Result:

How to calculate the Least Common Multiple (LCM)

Technique 1: Common Multiples

List the multiples of each number in ascending order: the first shared value is the LCM. This works well with small numbers; if they grow, switch to prime factorization.

Example: LCM of 4 and 6

Multiples of 4: 4, 8, 12, 16, 20...

Multiples of 6: 6, 12, 18, 24...

LCM(4, 6) = 12

Technique 2: prime factorization

Break each number into prime factors, take the highest exponent of each factor, and multiply those powers. The product is the LCM: this method suits large numbers or more than two integers.

Example: LCM of 12 and 18

12 = 2² × 3

18 = 2 × 3²

Take: 2² and 3²

LCM = 2² × 3² = 36

When is the LCM used in real life?

The Least Common Multiple appears in everyday situations where two or more cycles must coincide. Here are some concrete examples:

Transport: when do two buses meet?

One bus arrives every 12 minutes and another every 18 minutes. If both arrive at 8:00 AM, when will they meet again?

LCM(12, 18) = 36 minutes

Both buses will meet again at 8:36 AM.

More everyday examples:

Shift work: one employee rests every 4 days and another every 6 days. When will their days off coincide? LCM(4, 6) = 12 days.
School math: to add fractions with different denominators (e.g., 1/4 + 1/6), you need the LCM of the denominators as the common denominator.