About GCF & LCM Calculator
This calculator finds the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of any two positive integers. It shows the prime factorization of each number, the GCF derived from those factors, and the LCM calculated using the formula LCM = (n₁ × n₂) / GCF. It also verifies the result by confirming that GCF × LCM equals the product of the two input numbers. Understanding GCF and LCM is essential for simplifying fractions, solving ratio and proportion problems, scheduling events that repeat on different cycles, and working with modular arithmetic. Students encounter these concepts in pre-algebra and number theory, while programmers use them for everything from array alignment to cryptographic algorithms. The comprehensive output — including the prime factor breakdown — makes this tool equally valuable for learning and for quick reference. Whether you are finding a common denominator, planning synchronized timetables, or exploring the properties of numbers, this calculator provides reliable answers with full transparency into the underlying math.