LCM & GCD (GCF) Calculator with Prime Factorization
Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD / GCF) for any set of integers. Review step-by-step solutions using the Euclidean division algorithm and prime factor decomposition trees.
How to Use LCM & GCD / GCF Calculator
Input Numbers
Enter two or more positive integers separated by commas or spaces (e.g., 24, 36, 60).
Calculate
Click Calculate to view both LCM and GCD results simultaneously.
Examine Method
Review the prime factor breakdown and step-by-step Euclidean division table.
About LCM & GCD / GCF Calculator
The Greatest Common Divisor (GCD) is the largest integer that divides all input numbers without remainder. The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all input numbers. The Euclidean algorithm solves GCD in logarithmic time using repeated remainder division.
Key Features
- Calculates both LCM and GCD/GCF simultaneously for 2 to 10 numbers
- Prime factorization method displaying exponent notation for each prime factor
- Euclidean division algorithm steps for rapid two-number GCD resolution
- Formula relationship: LCM(a, b) = (|a × b|) / GCD(a, b)
- Instant copy of results and prime factor breakdown
Frequently Asked Questions
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