Another Look at Least Common Multiple and Greatest Common Factor

1978 ◽  
Vol 25 (6) ◽  
pp. 52-53
Author(s):  
Loren L. Henry
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Common Factor ◽  
Middle School Mathematics ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Prime Factorization ◽  
Problem Solving Skills ◽  
Whole Numbers ◽  
Main Disadvantage

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.

Reflection Borders for Patchwork Quilts

1986 ◽  
Vol 79 (2) ◽  
pp. 138-143
Author(s):  
Duane DeTemple
Keyword(s):  
Problem Solving ◽  
Basic Program ◽  
Greatest Common Divisor ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Problem Solving Skills ◽  
General Proof ◽  
Special Cases ◽  
Fertile Area

The question posed in this article provides an unexpectedly fertile area in which students can test their problem-solving skills. The problem is easily stated and understood, and special cases can be quickly generated as a source of conjectures and possible counterexamples. The solution is elusive but elegantly simple, and students may well guess the answer long before they produce a general proof. The solution involves the concepts of least common multiple and greatest common divisor, even though the problem itself is essentially a geometric one. An appendix by James H. Jordan lists an Apple BASIC program that permits students to experiment and gather data by means of microcomputer graphics. Figures 1 and 2 are printouts from this program.

Expanding participation in problem solving in a diverse middle school mathematics classroom

2010 ◽  
Vol 22 (1) ◽  
pp. 91-118 ◽  
Author(s):  
Keith Weber ◽  
Iuliana Radu ◽  
Mary Mueller ◽  
Arthur Powell ◽  
Carolyn Maher
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Classroom ◽  
Middle School Mathematics ◽  
School Mathematics

scholarly journals The Implementation of APIQ Creative Mathematics Game Method in the Subject Matter of Greatest Common Factor and Least Common Multiple in Elementary School

2017 ◽  
Author(s):  
Ansari Saleh Ahmar ◽  
Abdul Rahman ◽  
Andi Nurani Mangkawani Arifin ◽  
Dewi Satria Ahmar ◽  
M. Agus ◽  
...  
Keyword(s):  
Elementary School ◽  
Subject Matter ◽  
Common Factor ◽  
Traditional Learning ◽  
Learning Method ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Causal Factors ◽  
Learning Mathematics ◽  
The Subject

One of causal factors for uninterested feeling of the students in learning mathematics is a monotonous learning method, like in traditional learning method. One of the ways for motivating students to learn mathematics is by implementing APIQ (Aritmetika Plus Intelegensi Quantum) creative mathematics game method. The purposes of this research are (1) to describe students’ responses toward the implementation of APIQ creative mathematics game method on the subject matter of Greatest Common Factor (GCF) and Least Common Multiple (LCM) and (2) to find out whether by implementing this method, the student’s learning completeness will improve or not. Based on the results of this research, it is shown that the responses of the students toward the implementation of APIQ creative mathematics game method in the subject matters of GCF and LCM were good. It is seen in the percentage of the responses were between 76-100%. (2) The implementation of APIQ creative mathematics game method on the subject matters of GCF and LCM improved the students’ learning.

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