Least Common Multiple Calculator (LCM)

Enter the set of numbers separated by a comma (,) in the box below to calculate the least common multiple (LCM), with step-by-step results, techniques for calculating the LCM and practical examples.

There is an error in the entered numbers

LCM =

Step-by-step result:

1. Prime factorization:

2. Taking factors with the highest exponent:

3. Result:

You might be interested in:

Fraction Calculator Calculate Percentage Proportion Calculator

How to calculate the LCM step by step

Technique 1: Common Multiples

List the multiples of each number until you find the first one in common. 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 Factors

Decompose each number into prime factors, take each factor with its highest exponent and multiply them. 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: LCM of common numbers

NumbersLeast 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 comes every 12 minutes and another every 18 minutes. If both pass at 8:00 AM, when will they coincide again?

LCM(12, 18) = 36 minutes

Both buses will coincide again at 8:36 AM.

More everyday examples:

  • Cooking: one recipe needs baking every 15 min and another every 20 min. When will both be ready at the same time? MCM(15, 20) = 60 min.
  • Shift work: one employee rests every 4 days and another every 6. When will their days off coincide? MCM(4, 6) = 12 days.
  • School math: to add fractions with different denominators (e.g. 1/4 + 1/6) you need the LCM of the denominator as the common base.