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

1. Oct 8, 2017

### awholenumber

LCM of

Numbers
Fractions
Rational expressions

GCF of

Numbers
Fractions
Rational expressions

2. Oct 8, 2017

### QuantumQuest

Do you mean the whole thing from the ground up or for which grade(s)?

3. Oct 8, 2017

### awholenumber

Yes , from the beginning .These are all the only things i am trying to learn ,nothing more .

4. Oct 8, 2017

5. Oct 8, 2017

### awholenumber

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 ?

6. Oct 8, 2017

### Staff: Mentor

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.

7. Oct 8, 2017

### awholenumber

Mark44
I understand this now .
Thanks a lot for the detailed explanations .