Another Look at Least Common Multiple and Greatest Common Factor

Abstract

Most contemporary middle school mathematics programs use the notion of prime factorization to obtain the least common multiple and the greatest common factor of a pair of natural or whole numbers. Success in determining the least common multiple or greatest common factor for a pair of numbers then depends on the ability to obtain the prime factorization for any given number. The main disadvantage of this approach arises when either of the pair of numbers is quite large. For example, determining the least common multiple of 2464 and 7469 by prime factorization involves knowledge of divisibility tests for primes and of the primes themselves. The purpose of this paper is to examine another method for obtaining the least common multiple and greatest common factor of a pair of numbers without using prime factorization. These methods provide opportunities for students to make and test conjectures about the possible generalizations of the results to more than two numbers. Such conjecturing should aid students in developing problem-solving skills.