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GCF and LCM Calculator
Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 2–6 numbers using prime factorization with full step-by-step explanations.
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Enter 2–6 numbers to find their GCF and LCM
Key Features — GCF and LCM Calculator
GCF for up to 6 numbers
LCM for up to 6 numbers
Prime factorization of each number
Exponential notation display
Step-by-step derivation of GCF and LCM
Dynamic number input
Why Use This Tool — GCF and LCM Calculator
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Frequently Asked Questions — GCF and LCM Calculator
What is the GCF (Greatest Common Factor)?
The GCF (also called GCD — Greatest Common Divisor) is the largest positive integer that divides each of the given numbers without a remainder. GCF(12, 18) = 6 because 6 is the largest number that divides both 12 and 18.
What is the LCM (Least Common Multiple)?
The LCM is the smallest positive integer that is evenly divisible by each of the given numbers. LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6. LCM is useful for adding fractions with different denominators.
How are GCF and LCM related?
For two numbers a and b: GCF(a,b) × LCM(a,b) = a × b. This relationship is useful for quick calculations. For example, GCF(4,6) = 2, LCM(4,6) = 4×6/2 = 12.