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LCM Calculator

Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of up to 10 numbers with step-by-step prime factorization method.

LCM & GCF Results

Numbers -
LCM (Least Common Multiple) 0
GCF (Greatest Common Factor) 0

Prime Factorization Method

How to Use the LCM Calculator

  1. Enter up to 10 numbers separated by commas or spaces.
  2. Click "Calculate LCM & GCF" to find the results.
  3. Review the LCM (smallest number that is a multiple of all inputs).
  4. Review the GCF (largest number that divides all inputs evenly).
  5. See the step-by-step prime factorization method.

Formulas Used

Prime Factorization Method for LCM:

1. Find prime factors of each number

2. Take the highest power of each prime factor

3. Multiply these together to get LCM

Using GCF:

LCM(a, b) = (a × b) / GCF(a, b)

For multiple numbers:

LCM(a, b, c) = LCM(LCM(a, b), c)

Frequently Asked Questions

What is LCM?

LCM (Least Common Multiple) is the smallest positive integer that is divisible by all given numbers. It's used for finding common denominators, aligning periodic events, and solving problems involving synchronization.

How is LCM different from GCF?

LCM finds the smallest number that all given numbers divide into evenly. GCF finds the largest number that divides all given numbers evenly. For example, LCM(4, 6) = 12, but GCF(4, 6) = 2.

When would I use LCM in real life?

LCM is used when: finding when events will coincide (e.g., two buses arriving at the same time), finding common denominators for fractions, scheduling recurring meetings, determining when gears will align, and solving problems involving periodic patterns.

What is the prime factorization method?

The prime factorization method breaks each number down into its prime factors. The LCM is found by taking each unique prime factor to its highest power across all numbers and multiplying them together. This method shows the mathematical structure behind the LCM.

Can I calculate LCM of more than 2 numbers?

Yes! Our calculator supports up to 10 numbers. The LCM of multiple numbers is found by iteratively calculating LCM(LCM(a, b), c), and so on. The prime factorization method naturally extends to any number of inputs.