Bridging theory and application: An in-depth study of the greatest common divisor and least common multiple in mathematics and real-world settings

Abstract

The study of the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD) explores the fundamental field of number theory. In addition to being essential to theoretical number theory, these mathematical ideas have extensive applications in computer science, algebra, and real-world settings like network routing and scheduling. Using techniques like the Euclidean algorithm for GCD calculation and prime factorization for LCM, the study starts by examining the fundamental concepts and notations of GCD and LCM. Then the author goes further into the detail about how these ideas are used to polynomial equations, highlighting how they may be used to solve challenging issues and simplify algebraic expressions. The studys practical applications, which demonstrate how GCD and LCM optimize scheduling tasks and boost network routing efficiency, are presented in the conclusion. The results of this study highlight the broad impact and adaptability of LCM and GCD in theoretical and applied mathematics, providing valuable insights for further research in these domains.