Which book to buy to learn all these? (LCM, GCF)

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Discussion Overview

The discussion revolves around learning the concepts of Least Common Multiple (LCM) and Greatest Common Factor (GCF), specifically focusing on their application to numbers, fractions, and rational expressions. Participants seek recommendations for resources or books to facilitate this learning.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant inquires about learning LCM and GCF from the ground up, specifying their focus on these topics alone.
  • Another participant recommends a workbook aimed at grades 4 to 6 as a simple resource for learning about factors, factoring, GCF, and LCM.
  • Several participants share procedures for calculating LCM and GCF, emphasizing the use of prime factorization and the importance of identifying common and all factors.
  • There is a discussion about the application of LCM and GCF to fractions and rational expressions, noting that these concepts are typically applied to the denominators of such expressions for combination purposes.
  • Examples are provided to illustrate the calculation of LCM and GCF for both numerical and algebraic expressions.
  • One participant expresses gratitude for the detailed explanations provided in the thread, indicating a clearer understanding of the concepts.

Areas of Agreement / Disagreement

Participants generally agree on the procedures for calculating LCM and GCF, but there is some uncertainty regarding the application of these concepts to fractions and rational expressions, as it is noted that this is not a common practice.

Contextual Notes

The discussion includes various methods and examples for calculating LCM and GCF, but it does not resolve the question of how to approach these concepts in the context of fractions and rational expressions, leaving some assumptions and definitions unaddressed.

Who May Find This Useful

Individuals seeking to learn about LCM and GCF, particularly students or educators looking for resources and explanations at an introductory level.

awholenumber
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LCM of

Numbers
Fractions
Rational expressions

GCF of

Numbers
Fractions
Rational expressions
 
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Do you mean the whole thing from the ground up or for which grade(s)?
 
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Yes , from the beginning .These are all the only things i am trying to learn ,nothing more .
 
In a pdf online , i found this .LCM
1.
Find the prime factorization of each
number in the group.
2.
Make a list of ALL factors, raised
to the HIGHEST power that appears in
any factorization.
3.
Multiply out.

GCF

1.
Find the prime factorization of each
number in the group.
2.
Make a list of COMMON factors,
raised to the LOWEST power that
appears in any factorization.
3.
Multiply out

That's it ?
 
awholenumber said:
In a pdf online , i found this .LCM
1.
Find the prime factorization of each
number in the group.
2.
Make a list of ALL factors, raised
to the HIGHEST power that appears in
any factorization.
3.
Multiply out.

GCF

1.
Find the prime factorization of each
number in the group.
2.
Make a list of COMMON factors,
raised to the LOWEST power that
appears in any factorization.
3.
Multiply out

That's it ?
These procedures are for finding the LCM (least common multiple) of two or more numbers or the GCF (greatest common factor) of two or more numbers.

In post 1 you asked about the LCM of fractions and rational expression, and the GCF of fractions and rational expression. We don't ordinarily try to find the LCM or GCF of fractions or rational expressions, but we apply these concepts to the denominators of fractions and rational expressions so that we can combine two or more of these expression.

The LCM of a set of numbers or expressions is the smallest expression that is evenly divisible by all members of the set.
Ex. 1: The LCM of 4, 10 and 25 is 100.
4 = 22
10 = 2 * 5
25 = 52
The LCM has to have two factors of 2 and two factors of 5, or 2 * 2 * 5 * 5 = 100

Ex. 2. The LCM of x - 2, 2x - 4 and x2 = 4 is 2(x2 - 4)
x - 2 is already simplified
2x - 4 = 2(x - 2)
x2 - 4 = (x - 2)(x + 2)
The LCM has to contain one factor of x - 2, a factor of 2, and a factor of x + 2, or 2(x - 2)(x + 2) = 2(x2 - 4)

The GCF is used to find the largest expression that evenly divides a set of numbers or expressions.
Ex. 3 The GCF of 40 and 100 is 20.
40 = 23 * 5
100 = 22 * 52
The least number of times 2 appears in both numbers is twice; the least number of times 5 appears is once, so the GCF = 22 * 5 = 20.

The process works in a similar way for algebraic expressions.
 
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Mark44
I understand this now .
Thanks a lot for the detailed explanations .
 

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