GCF & LCM Calculator
Find the Greatest Common Factor and Least Common Multiple of any numbers with prime factorization steps.
How to Use the GCF & LCM Calculator
- Enter the first whole number.
- Enter the second whole number.
- Click Calculate GCF & LCM to see both results instantly.
- Review the prime factorization of each number and the step-by-step method shown below the results.
Formula & Method
GCF (Greatest Common Factor) is found with the Euclidean algorithm: repeatedly replace the larger number by the remainder of dividing the two, until the remainder is zero.
LCM (Least Common Multiple) uses the relationship: LCM(a, b) = (a x b) / GCF(a, b)
For any two positive integers, GCF x LCM always equals the product of the two numbers.
Examples
| Number A | Number B | GCF | LCM |
|---|---|---|---|
| 12 | 18 | 6 | 36 |
| 48 | 180 | 12 | 720 |
| 7 | 13 | 1 | 91 |
| 24 | 36 | 12 | 72 |
| 100 | 75 | 25 | 300 |
Frequently Asked Questions
What is the GCF?
The Greatest Common Factor (also called GCD or HCF) is the largest number that divides both numbers exactly. For 12 and 18, the GCF is 6.
What is the LCM?
The Least Common Multiple is the smallest number that both numbers divide into exactly. For 12 and 18, the LCM is 36.
When do I use GCF vs LCM?
Use GCF when splitting things into equal groups or simplifying fractions. Use LCM when finding common denominators or scheduling repeating events.
What if the GCF is 1?
The numbers are called coprime (relatively prime) — they share no common factors. Their LCM is simply their product. Example: 7 and 13.
Does GCF x LCM always equal a x b?
Yes, for any two positive integers: GCF(a,b) x LCM(a,b) = a x b. This identity lets you find one from the other.
People Also Ask
What is the GCF of 48 and 180?
The GCF of 48 and 180 is 12. Prime factors of 48 are 2x2x2x2x3 and of 180 are 2x2x3x3x5; the shared factors 2x2x3 give 12.
What is the LCM of 12 and 18?
The LCM of 12 and 18 is 36. Multiples of 12: 12, 24, 36... Multiples of 18: 18, 36... The first common multiple is 36.
How do you find GCF using prime factorization?
Factor both numbers into primes, then multiply only the shared prime factors (using the lowest power of each). For 24 (2^3 x 3) and 36 (2^2 x 3^2): GCF = 2^2 x 3 = 12.