LCM & GCD Calculator
Calculate the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of two or more numbers instantly, with step-by-step prime factorization.
Least Common Multiple (LCM)
Enter two or more positive integers separated by commas or spaces.
LCM vs GCD
GCD (Greatest Common Divisor) — also called HCF — is the largest number that divides all the given numbers without a remainder. Found by taking the product of shared prime factors.
LCM (Least Common Multiple) is the smallest number that is a multiple of all given numbers. Found by taking the product of all prime factors at their highest power.
Relationship: LCM(a, b) × GCD(a, b) = a × b.
Use GCD for simplifying fractions. Use LCM for adding fractions (finding a common denominator) or scheduling recurring events.
Frequently Asked Questions
The Greatest Common Divisor (GCD), also called HCF or GCF, is the largest positive integer that divides all of the given numbers. For example, GCD(12, 18) = 6.
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. For example, LCM(4, 6) = 12.
For two numbers a and b: LCM(a, b) = (a × b) / GCD(a, b). Knowing one lets you quickly find the other.
LCM is used when adding or subtracting fractions (to find the common denominator), and for scheduling problems like finding when recurring events coincide.
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