GCF and LCM Calculator - Find Both Values
Calculate both the Greatest Common Factor and Least Common Multiple at once. Enter two or more numbers to find GCF and LCM with step-by-step solutions.
Formula
LCM(a,b) = |a×b| / GCF(a,b)
The LCM is the product of the numbers divided by their GCF. The GCF is the largest shared divisor.
Worked Examples
Example 1: GCF & LCM of 12 and 18
Problem:Find values for 12, 18
Solution:Factors of 12: 1,2,3,4,6,12. Factors of 18: 1,2,3,6,9,18. Common: 1,2,3,6. GCF=6. \nMultiples of 12: 12,24,36... Multiples of 18: 18,36... LCM=36.
Result:GCF: 6, LCM: 36
Example 2: Coprime Numbers
Problem:Find values for 8 and 9
Solution:8 (2³) and 9 (3²) share no factors. GCF=1. LCM = 8×9 = 72.
Result:GCF: 1, LCM: 72
Frequently Asked Questions
What is the difference between GCF and GCD?
They are the same thing. GCF stands for Greatest Common Factor, and GCD stands for Greatest Common Divisor.
Can GCF be 1?
Yes. If the numbers share no common factors other than 1, they are called "relatively prime" or "coprime" (e.g., 8 and 15).
How do I find the LCM of more than two numbers?
Find the LCM of the first two numbers, then find the LCM of that result and the third number, and so on.
Can GCF be larger than LCM?
No. GCF is a factor (smaller or equal), and LCM is a multiple (larger or equal). Thus, GCF ≤ LCM.