GCF & LCM Calculator
How It Works
This gcf & lcm calculator uses established formulas to provide accurate results.
The basic rule:
- GCF × LCM = a × b
- LCM(a, b) = (a × b) / GCF(a, b)
- Euclidean algorithm: GCF(a, b) = GCF(b, a mod b)
Results are estimates. Consult a professional for critical decisions.
Frequently Asked Questions
What is the greatest common factor (GCF)?
The GCF is the largest number that divides evenly into two or more numbers. For example, the GCF of 24 and 36 is 12, because 12 is the largest number that divides into both 24 and 36 without a remainder.
What is the least common multiple (LCM)?
The LCM is the smallest positive number that is a multiple of two or more numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
How are GCF and LCM related?
For any two numbers a and b: GCF(a,b) × LCM(a,b) = a × b. This relationship can help you find one if you know the other.
When do you use GCF and LCM?
Use GCF when simplifying fractions (divide numerator and denominator by GCF). Use LCM when finding common denominators to add or subtract fractions.