Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 2–4 numbers using prime factorization or the Euclidean algorithm. View factor breakdown tables and step-by-step solutions.
The Greatest Common Factor (GCF) and Least Common Multiple (LCM) are two of the most fundamental concepts in number theory and arithmetic. The GCF of two or more integers is the largest positive integer that divides each of them without a remainder. The LCM is the smallest positive integer that is divisible by each of them. These values are essential for simplifying fractions, finding common denominators, solving word problems, and working with ratios.
Our GCF & LCM calculator supports 2 to 4 numbers at once and offers two methods: prime factorization and the Euclidean algorithm. The prime factorization method breaks each number into its prime components and identifies shared and combined factors. The Euclidean algorithm uses repeated division to efficiently compute the GCD. The calculator displays a detailed prime factorization table showing the power of each prime factor across all inputs, making it easy to see which factors are shared. Visual comparison bars and step-by-step solutions help you understand the process, not just the answer. Whether you are simplifying fractions in a math class or solving scheduling problems in real-world applications, this tool delivers instant, accurate results.
GCF & LCM Calculator helps you solve gcf & lcm problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter Number A, Number B, Number C (optional) once and immediately inspect GCF (Greatest Common Factor), LCM (Least Common Multiple), GCF Factorization to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
GCF uses the minimum exponent of each common prime factor. LCM uses the maximum exponent of each prime factor. For two numbers a, b: a × b = GCF(a, b) × LCM(a, b).
Result: GCF (Greatest Common Factor) shown by the calculator
Using the preset "12, 18", the calculator evaluates the gcf & lcm setup, applies the selected algebra rules, and reports GCF (Greatest Common Factor) with supporting checks so you can verify each transformation.
This calculator takes Number A, Number B, Number C (optional), Number D (optional) and applies the relevant gcf & lcm relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use GCF (Greatest Common Factor), LCM (Least Common Multiple), GCF Factorization, LCM Factorization to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
They are the same thing. GCF stands for Greatest Common Factor, while GCD stands for Greatest Common Divisor. Both refer to the largest number that divides all given numbers evenly.
Find the GCF of the first two numbers, then find the GCF of that result with the third number, and so on. GCF(a, b, c) = GCF(GCF(a, b), c).
LCM is useful for scheduling problems (e.g., when will two events coincide again), finding common denominators in fractions, and determining repeating patterns in cycles.
By convention, GCF and LCM are always positive. The calculator uses the absolute values of your inputs to compute them.
GCF(a, 0) = a for any nonzero a. LCM involving 0 is typically defined as 0. Enter positive integers for meaningful results.
Because the GCF captures shared prime factors (with minimum exponents) and the LCM captures all prime factors (with maximum exponents). Together they account for each factor exactly as many times as it appears in the product.