Common Factor Calculator
Calculate Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers. Visualize common factors.
Numbers
Simplify Fraction
Simplified Fraction
48/64
3/4
GCD: 16
Greatest Common Divisor (GCD)
12
Least Common Multiple (LCM)
72
Common Factors
All Factors
Factors of 24
Factors of 36
Prime Factorization
Calculation
GCD Formula
GCD = product of common factors with lowest exponent
LCM Formula
LCM = product of all factors with highest exponent
Relationship
GCD(a,b) × LCM(a,b) = a × b
12 × 72 = 864
Greatest Common Divisor
The GCD of two or more numbers is the largest number that divides all of them exactly. It can be calculated by factoring and taking common factors with the lowest exponent, or using Euclid's algorithm.
Least Common Multiple
The LCM is the smallest number that is a multiple of all given numbers. It's calculated by taking all prime factors with their highest exponent. LCM(a,b) = (a × b) / GCD(a,b).
Euclidean Algorithm
Efficient method to calculate GCD: divide the larger by the smaller, then divide the divisor by the remainder, repeat until remainder is 0. The last divisor is the GCD.