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

  1. Oct 8, 2017 #1
    LCM of

    Numbers
    Fractions
    Rational expressions

    GCF of

    Numbers
    Fractions
    Rational expressions
     
  2. jcsd
  3. Oct 8, 2017 #2

    QuantumQuest

    User Avatar
    Gold Member

    Do you mean the whole thing from the ground up or for which grade(s)?
     
  4. Oct 8, 2017 #3
    Yes , from the beginning .These are all the only things i am trying to learn ,nothing more .
     
  5. Oct 8, 2017 #4

    QuantumQuest

    User Avatar
    Gold Member

  6. Oct 8, 2017 #5
    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 ?
     
  7. Oct 8, 2017 #6

    Mark44

    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.
     
  8. Oct 8, 2017 #7
    Mark44
    I understand this now .
    Thanks a lot for the detailed explanations .
     
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