GCF & LCM Calculator
GCF & LCM Calculator
About GCF & LCM Calculator
GCF and LCM Explained
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest number that divides evenly into all given numbers. The GCF of 12 and 18 is 6. The Least Common Multiple (LCM) is the smallest number that is a multiple of all given numbers. The LCM of 4 and 6 is 12. GCF is used for simplifying fractions, while LCM is used for finding common denominators, scheduling recurring events, and solving problems involving cycles.
How They Are Calculated
The most efficient method is the Euclidean algorithm for GCF: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. The last non-zero remainder is the GCF. Once you have the GCF, find LCM using: LCM(a,b) = |a x b| / GCF(a,b). The prime factorization method also works: GCF uses the lowest power of shared primes, LCM uses the highest power of all primes present.
How to Use This Calculator
Enter two or more numbers separated by commas or in separate fields. Click Calculate to see both the GCF and LCM along with the prime factorization of each number. The step-by-step Euclidean algorithm solution is shown so you can understand the process.
Frequently Asked Questions
What is the relationship between GCF and LCM?
For any two numbers a and b: GCF(a,b) x LCM(a,b) = a x b. This means if you know one, you can find the other easily.
When do I use GCF vs LCM?
Use GCF for simplifying fractions, dividing things into equal groups, and finding shared factors. Use LCM for common denominators, scheduling problems, and finding when cycles synchronize.
Can GCF be calculated for more than two numbers?
Yes. Find GCF of the first two numbers, then find GCF of that result with the third number, and so on. The same chaining approach works for LCM.
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