LCM Calculator Online

Calculate the least common multiple (LCM) of two or more positive integers. Enter numbers separated by commas (,) to see the result, prime factorization, and every calculation step.

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LCM =

Result and step-by-step working:

1. Prime factorization:

2. Select the factors with the highest exponent:

3. Result:

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How to calculate the LCM step by step

Technique 1: Common Multiples

List the multiples of each number until you find the first common multiple. This is ideal for small numbers.

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 down into prime factors, select the highest power of each factor, and multiply the selected factors. This is ideal for large numbers or more than two numbers.

Example: LCM of 12 and 18

12 = 2² × 3

18 = 2 × 3²

Take: 2² and 3²

LCM = 2² × 3² = 36

Reference table: least common multiple

Numbers Least Common Multiple (LCM)
2, 44
3, 66
4, 612
6, 824
6, 918
8, 1224
12, 1836
18, 2472
24, 3672

When is the LCM used in real life?

The LCM 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:

  • Cooking: one recipe needs baking every 15 minutes and another every 20 minutes. When will both be ready at the same time? LCM(15, 20) = 60 minutes.
  • 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.