Least Common Multiple Calculator

Use this calculator to find the least common multiple (LCM) of two or more numbers. Get step-by-step solutions and understand how LCM is calculated.

Least Common Multiple Calculator

Enter two or more numbers separated by commas, then click Calculate to find their least common multiple (LCM).

Result

What is the Least Common Multiple (LCM)?

The Least Common Multiple (LCM) of two or more numbers is the smallest positive number that is divisible by all of them without a remainder.

For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide into evenly.

Methods to Find the LCM

Prime Factorization Method

This method involves finding the prime factorization of each number, then multiplying the highest power of each prime factor that appears in any of the numbers.

Example: To find LCM(12, 18)
1. Prime factorization: 12 = 2² × 3, 18 = 2 × 3²
2. Take the highest power of each prime factor: 2² and 3²
3. Multiply them: 2² × 3² = 4 × 9 = 36
Therefore, LCM(12, 18) = 36

Using the GCD/GCF Method

The LCM can also be calculated using the relationship between LCM and GCD (Greatest Common Divisor):

LCM(a, b) = (a × b) ÷ GCD(a, b)

Example: To find LCM(12, 18)
1. Find GCD(12, 18) = 6
2. Calculate: (12 × 18) ÷ 6 = 216 ÷ 6 = 36
Therefore, LCM(12, 18) = 36

Applications of LCM

  • Finding common time periods (e.g., when two events will coincide again)
  • Working with fractions (finding common denominators)
  • Solving scheduling and synchronization problems
  • Optimizing resource allocation in computer science

How to Use This Calculator

  1. Enter two or more positive integers separated by commas in the input field.
  2. Click the 'Calculate' button to find the LCM.
  3. View the result and the step-by-step solution explaining how the LCM was calculated.
  4. Click 'Clear' to reset the calculator and perform a new calculation.