Sharing Teaching Ideas

1988 ◽  
Vol 81 (8) ◽  
pp. 648-652
Author(s):  
Paul A. Klein
Keyword(s):  
Common Factor ◽  
Common Denominator ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Prime Factors ◽  
Instructional Sequences ◽  
Teaching Ideas

Few arithmetic skills have eluded as many students as those used in reducing fractions or in obtaining the least common denominator of two fractions. In the more popular instructional sequences the general concepts of greatest common factor (GCF) and least common multiple (LCM) are developed first Usually, these concepts involve the decomposition of the numbers into prime factors as shown in example 1.

A simplified presentation for finding the LCM and the GCF

1974 ◽  
Vol 21 (5) ◽  
pp. 415-416
Author(s):  
Laurence Sherzer
Keyword(s):  
Common Factor ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Prime Factors ◽  
Positive Integers

Given the prime factors of two positive integers, the least common multiple (LCM) of these two numbers is the product of the union of these prime factors, and the greatest common factor (GCF) is the product of the intersection of these prime factors. If we could just state this fact to our students and be understood, our job of teaching them to find the LCM or the GCF of two numbers would be greatly simplified. Unfortunately, as in most teaching, simple verbal statements do not suffice.

Geometric Figures Make the LCM Obvious

1987 ◽  
Vol 34 (7) ◽  
pp. 17-18
Author(s):  
Flo McEnery Edwards
Keyword(s):  
Common Factor ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Geometric Figures ◽  
Prime Factors

The greatest common factor (GCF) is easily found by comparing the prime factors of a set of numbers and choosing the prime factors they have in common. The least common multiple (LCM) is often more difficult for students to find. The prime factors of the LCM are not necessarily common to a set of numbers, but their product i a common multiple of those numbers. According to Troutman and Lichtenberg (1982, 173), “the least multiple that is common to some set of numbers will have all the factors of those numbers and no other factors.” How, then, is it possible to find these prime factors just by inspection? One way is to write the prime factors of a set of numbers in a list and use geometric figures to find the prime factors of the LCM.

A Variation on the Algorithm for GCD and LCM

1982 ◽  
Vol 30 (3) ◽  
pp. 46
Author(s):  
Verna M. Adams
Keyword(s):  
Prime Numbers ◽  
Prime Divisors ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Prime Factors

An algorithm sometimes presented for finding the least common multiple (LCM) of two numbers uses tbe technique of simultaneously finding the prime factors of the numbers. This technique is shown in figure 1. Both numbers are checked for divisibility by 2, then by 3, by 5, and so on. If the divisor does not divide one of the numbers, the number is written on the next line as shown in steps 4 and 5. This process continues until all numbers to the left and on the bottom are prime numbers, or it can be continued, as shown in figure 1, until the numbers across the bottom are all ones. The least common multiple is the product of all of the prime divisors. Thus, LCM (80, 72) = 24 · 32 · 5.

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.

Sound Off!: Least Common Denominators and the Common Core

2013 ◽  
Vol 106 (7) ◽  
pp. 488-490 ◽  
Author(s):  
J. Bradford Burkman
Keyword(s):  
Common Core ◽  
Common Core State Standards ◽  
Common Factor ◽  
State Standards ◽  
School Level ◽  
Common Denominator ◽  
Core State ◽  
High School Level ◽  
Least Common Multiple ◽  
The Common

The Common Core State Standards do not expect students to make connections between the greatest common factor, least common multiple, and least common denominator. The author discusses implications for student learning, including at the high school level, and makes a suggestion for higher expectations in interpreting and implementing the CCSS.

Greatest Common Factor and Least Common Multiple

1984 ◽  
Vol 31 (8) ◽  
pp. 43-44
Author(s):  
Charles E. Lamb ◽  
Lyndal R. Hutcherson
Keyword(s):  
Common Factor ◽  
Computational Algorithms ◽  
Common Multiple ◽  
Least Common Multiple

The greatest common factor and the least common multiple are two concepts that are important in their own right as well as crucial to the development of other topics in mathematics. Unfortunately, these two topics can be difficult for students to understand even apart from the process of computing numerical values for them. This article discusses some strategies for avoiding misconceptions of these ideas and reviews some computational algorithms for them.

Teacher to Teacher: Finding Common Ground

1999 ◽  
Vol 5 (4) ◽  
pp. 236
Author(s):  
Elizabeth H. Bradley
Keyword(s):  
Common Ground ◽  
Common Factor ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Visual Aid

IF YOUR STUDENTS CONFUSE GREATEST common factor (GCF) with least common multiple (LCM), try this approach, which employs a diagram as a visual aid and can be used to reduce fractions.

LH LABELING OF GRAPHS

2021 ◽  
Vol 10 (4) ◽  
pp. 2167-2179
Author(s):  
M. Farisa ◽  
K.S. Parvathy
Keyword(s):  
Common Factor ◽  
Natural Numbers ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Bijective Function

A graph $G$ with $n$ vertices is said to have an LH labeling if there exists a bijective function $f: V(G)$ to $\{1,2,3,\ldots ,n\} $ such that the induced map $f^*: E(G)\rightarrow N$, the set of natural numbers defined by $f^*(uv) = \frac{LCM(f(u), f(v))} {HCF(f(u),f(v))}$ is injective (LCM and HCF denotes the least common multiple and highest common factor respectively). A graph that admits an LH labeling is called an LH graph. This article explores the results of LH Labeling of some standard graphs.

On Nonsingular Power LCM Matrices

2006 ◽  
Vol 13 (04) ◽  
pp. 689-704 ◽  
Author(s):  
Shaofang Hong ◽  
K. P. Shum ◽  
Qi Sun
Keyword(s):  
Singular Number ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Closed Set ◽  
Prime Factors ◽  
The Matrix ◽  
Lcm Matrix ◽  
Positive Integers ◽  
Power Lcm Matrix

Let e ≥ 1 be an integer and S={x1,…,xn} a set of n distinct positive integers. The matrix ([xi, xj]e) having the power [xi, xj]e of the least common multiple of xi and xj as its (i, j)-entry is called the power least common multiple (LCM) matrix defined on S. The set S is called gcd-closed if (xi,xj) ∈ S for 1≤ i, j≤ n. Hong in 2004 showed that if the set S is gcd-closed such that every element of S has at most two distinct prime factors, then the power LCM matrix on S is nonsingular. In this paper, we use Hong's method developed in his previous papers to consider the next case. We prove that if every element of an arbitrary gcd-closed set S is of the form pqr, or p2qr, or p3qr, where p, q and r are distinct primes, then except for the case e=1 and 270, 520 ∈ S, the power LCM matrix on S is nonsingular. We also show that if S is a gcd-closed set satisfying xi< 180 for all 1≤ i≤ n, then the power LCM matrix on S is nonsingular. This proves that 180 is the least primitive singular number. For the lcm-closed case, we establish similar results.

scholarly journals Pemanfaatan permainan tradisional untuk media pembelajaran: Congklak bilangan sebagai inovasi pembelajaran matematika sekolah dasar

2019 ◽  
Vol 15 (1) ◽  
pp. 14-22
Author(s):  
Christina Kartika Sari ◽  
Ana Muslihatun ◽  
Lutfianisa Cahyaningtyas ◽  
Rangga Narandera La Hasaleh Khaimmudin ◽  
Ridhy Nizar Fijatullah ◽  
...  
Keyword(s):  
Active Learning ◽  
Community Service ◽  
Mathematics Learning ◽  
Common Factor ◽  
Learning Approach ◽  
Service Program ◽  
Common Multiple ◽  
Least Common Multiple ◽  
Fourth Grade Students ◽  
Traditional Game

[Bahasa]: Kegiatan pengabdian ini bertujuan untuk mengenalkan Congklak Bilangan (COGAN) sebagai media pembelajaran matematika, khususnya materi Faktor Persekutuan Terbesar (FPB) dan Kelipatan Persekutuan Terkecil (KPK), dan upaya untuk membantu siswa dalam memahami konsep FPB dan KPK. Selain itu, kegiatan ini merupakan upaya untuk melestarikan permainan tradisional congklak. Sasaran kegiatan ini adalah siswa kelas IV Sekolah Dasar (SD) Negeri 3 Karangasem. Kegiatan dikemas mengunakan metode pelatihan dan pendampingan, dengan pendekatan participant active learning. Kegiatan dilaksanakan dalam lima tahapan, yakni penyampaian materi FPB dan KPK, pemutaran video untuk pengenalan congklak, pembuatan COGAN, penggunaan COGAN dalam pembelajaran FPB dan KPK, dan terakhir evaluasi kegiatan. Berdasarkan hasil survei pada akhir kegiatan pengabdian menunjukkan bahwa 84,6% siswa menyatakan desain COGAN menarik dan 88% siswa menyatakan bahwa pembelajaran matematika dengan COGAN berlangsung menyenangkan. Hasil pengabdian ini dapat menjadi alternatif bagi guru untuk mengenalkan konsep FPB dan KPK dalam pembelajaran matematika. Kata Kunci: congklak bilangan; media pembelajaran matematika; permainan tradisional [English]: This community service program aims to introduce Congklak Bilangan (COGAN) as a mathematics learning media for the greatest common factor (GCF) and least common multiple (LCM) topics and help students understand the concepts of GCF and LCM. Besides, this program is also an effort to preserve traditional game, Congklak. The subjects are fourth-grade students. The program was conducted by training and mentoring method which refers to the participant active learning approach. The program was done in five stages, namely teaching GFC and LCM topics, playing videos for the introduction of congklak, making COGAN, using COGAN in GFC and LCM learning, and having evaluation. Based on the post-training survey, 84.6% of students stated that the COGAN design is interesting and 88% of students agreed that learning with COGAN is fun. The results can be an alternative for teachers to introduce the concept of GCF and LCM in mathematics learning. Keywords: congklak bilangan, GCF and LCM; learning media; traditional game

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