๐ข GCF/LCM Calculator
Calculate the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of two numbers.
Enter values for A and B to display the prime factor comparison
Greatest Common Factor (GCF/GCD)
The largest number that is a common divisor of two or more numbers. Found by multiplying the minimum exponents of common prime factors.
GCF(12, 18) = GCF(2ยฒร3, 2ร3ยฒ) = 2ยนร3ยน = 6
Least Common Multiple (LCM)
The smallest number that is a common multiple of two or more numbers. Found by multiplying the maximum exponents of all prime factors.
LCM(12, 18) = 2ยฒร3ยฒ = 36
Euclidean Algorithm
An efficient algorithm for finding the GCF. Repeat until the remainder becomes 0.
GCF(a, b) = GCF(b, a mod b)
GCF(48, 18) โ GCF(18,12) โ GCF(12,6) โ GCF(6,0) = 6
GCF โ LCM Relationship
GCF(a,b) ร LCM(a,b) = a ร b
LCM(a,b) = a ร b รท GCF(a,b)
Applications
Used for simplifying fractions (GCF), finding common denominators (LCM), period problems, and tile layout optimization.