gcdlcm18

gcdlcm18 is an open-source library and reference implementation for computing the greatest common divisor and least common multiple of integers. It aims for correctness, portability, and simplicity, offering clean APIs and compact code suitable for education, competitive programming, and lightweight software that relies on precise gcd and lcm calculations.

The project originated in 2018 when a small team of programmers and educators sought a dependable teaching resource and a fast, language-agnostic core for gcd and lcm operations. The initial release provided core routines in C and C++, with bindings and documentation that encouraged community contributions and extensions.

Core algorithms include the Euclidean algorithm for normal inputs, enhanced variants such as binary gcd for performance on large data sets, and lifted implementations for 64-bit and arbitrary-precision arithmetic. The library handles signed and unsigned integers, protects against overflow with 128-bit intermediates when available, and includes an extended gcd function for solving linear Diophantine equations and modular inverses. Optional wrappers for Python, JavaScript, and other languages broaden accessibility.

gcdlcm18 is used as both a teaching aid and a practical tool in small projects and contests. The API emphasizes predictable behavior, clear documentation, and thorough testing, with example routines for arrays and streaming inputs and a small test suite to validate correctness across edge cases.

See also: greatest common divisor, least common multiple, Euclidean algorithm, binary GCD.