A classic textbook example — find the greatest common divisor of 12 and 18.
The greatest common divisor (GCD, also called GCF or HCF) is the largest number that divides both inputs evenly — computed here using the Euclidean algorithm, the same fast, ancient method taught in most math courses. The least common multiple (LCM) is the smallest number both inputs divide into evenly, computed from the GCD using the identity LCM(a,b) = |a×b| ÷ GCD(a,b).
Both figures are commonly needed for simplifying fractions (GCD) and finding a common denominator (LCM), among other uses.
The two numbers are "coprime" (or "relatively prime") — they share no common factors other than 1, even if neither number is itself prime.
Not directly here — for three or more numbers, compute the GCD or LCM of the first two, then combine that result with the next number, repeating as needed.
GCD and LCM are conventionally defined for positive integers — enter positive numbers here.