GCF & LCM Calculator

Find the Greatest Common Factor and Least Common Multiple of 2-10 numbers with step-by-step prime factorization.

Calculate GCF & LCM

Enter 2-10 positive integers, separated by commas
Verification
Prime Factorization
GCF: Common Prime Factors (lowest powers)
Take each common prime factor with its lowest exponent
LCM: All Prime Factors (highest powers)
Take each prime factor with its highest exponent
GCF

Frequently Asked Questions

What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF), also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest positive integer that divides each of the given numbers without leaving a remainder. For example, the GCF of 12 and 18 is 6.

What is the Least Common Multiple (LCM)?

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by each of the given numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.

How do you find GCF using prime factorization?

To find the GCF using prime factorization: 1) Find the prime factorization of each number, 2) Identify the common prime factors, 3) Multiply the common prime factors using the lowest power of each. For example, 12 = 2^2 x 3 and 18 = 2 x 3^2, so GCF = 2 x 3 = 6.

What is the relationship between GCF and LCM?

For any two positive integers a and b, the product of GCF and LCM equals the product of the two numbers: GCF(a,b) x LCM(a,b) = a x b. This relationship is useful for finding LCM when you know the GCF, or vice versa.