What Is the LCM and GCD Calculator?
GCD is the largest number that divides both a and b without remainder. LCM is the smallest number divisible by both.
How Does the LCM and GCD Calculator Work?
Euclid's algorithm computes GCD by repeated division. LCM = a × b / GCD.
LCM and GCD Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
The GCD (greatest common divisor) is found by repeatedly replacing the larger number with the remainder. The LCM follows from the identity LCM × GCD = a × b.
How to Use the LCM and GCD Calculator
- Enter two positive integers and the calculator returns both GCD and LCM with steps.
Step-by-Step Example Calculation
GCD and LCM of 12 and 18
Input Values:
a:12
b:18
Worked Steps: GCD(12, 18) = 6 and LCM(12, 18) = 36.
Understanding Your Result
GCD tells you the largest common factor for simplifying fractions. LCM tells you when two repeating events coincide.
Factors That Affect the Result
- Coprime numbers (sharing no common factor) have GCD = 1 and LCM = a × b.
When Should You Use This Calculator?
- Simplifying fractions, finding common denominators, scheduling recurring events.
Assumptions & Limitations
- Inputs must be positive integers up to 1 trillion.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Uses the classical Euclidean algorithm, which is exact for integers.