About LCM & GCF Calculator
When working with integers and fractions, two numbers appear constantly: The Greatest Common Factor (GCF) and the Least Common Multiple (LCM). These are the fundamental tools for simplifying math problems.
Greatest Common Factor (GCF)
Also known as the Greatest Common Divisor (GCD). It is the largest number that divides evenly into two or more numbers.
Use Case: Reducing fractions. To simplify 12/30, you find the GCF (which is 6) and divide top and bottom by it to get 2/5.
Least Common Multiple (LCM)
The smallest positive integer that is divisible by both numbers.
Use Case: Adding fractions. To add 1/4 + 1/6, you need a common denominator. The LCM of 4 and 6 is 12. So you convert to 3/12 + 2/12 = 5/12.
How to Use
Enter two integers (A and B). The tool runs the Euclidean Algorithm to find the GCF and uses the formula LCM(a,b) = |a*b| / GCF(a,b) to find the LCM instantly.