Greatest common factor, least common multiple.

Discussion in 'Math' started by strantor, Sep 20, 2011.

  1. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    I'm trying to help my neice with her homework over the internet, via her mom who's also trying to help her. I feel like I'm one of those idiots on "are you smarter than a 5th grader" So, here's what I got (this is the email I am sending her mom, with the homework questions in BOLD, and my answer in italics:
     
  2. Papabravo

    Expert

    Feb 24, 2006
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    Brian has 45 tanzas because:
    Code ( (Unknown Language)):
    1.  
    2. (4 * 11) +1 = 45 = (9*5)
     
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  3. djsfantasi

    AAC Fanatic!

    Apr 11, 2010
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    Start with: A*B=2,700

    Factor 2,700 into it's prime components:
    A*B=3*3*3*2*2*5*5

    Shuffling terms around using the knowledge we have that 3*5=15 is the greatest common multiple:
    A*B=(3*5)*(3*5)*2*2*3
    ..and introducing our friends x and y from algebra:
    A=15*x
    B=15*y

    ...and using the leftover terms,
    x*y=2*2*3

    This means there are multiple possibilities for the x and y values.
    x= 1, 2, 4
    y=12, 6, 3

    This results in:
    A= 15, 30, 60
    B=180, 90, 45

    Now using the three possible sets for x and y, I come up with three different answers, depending on which of the three perfectly valid choices we make for the 2 numbers whcih multiply together to get 2,700:
    A= 3*5 =15
    B= 2*2*3*3*5 =180
    Least common multiple =2*2*3*3*5 =180

    A= 2*3*5 =30
    B= 2*2*3*5*5 =90
    Least common multiple =2*2*3*5*5 =90

    A= 2*2*3*5 =60
    B= 3*3*5 =45
    Least common multiple =2*2*3*3*5 =180

    Your neice probably needs one correct answer. I like A=30 and B=90 because it stared me right in the face. In fact, I almost convinced myself it was the only answer.
     
  4. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    @djsfantasi
    I thought it was going to be a lot simpler than that. I think this stuff is supposed to be pre-algebra. Thanks for the answer, I will let her know.
     
  5. Zazoo

    Member

    Jul 27, 2011
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    One correction, of the remaining factors of 2*2*3 the pair of twos must remain in A or B, if you put a single two in both A and B then the GCF becomes 30 not 15. So the second one won't satisfy the required GCF
     
    Last edited: Sep 20, 2011
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  6. Georacer

    Moderator

    Nov 25, 2009
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    What's a tanza anyway?

    I 'd like to justify Papabravo's answer:

    We know that:
    11 \cdot N +1 =9 \cdot K \text{, where }N,K \in \mathbb{N} \Leftrightarrow<br />
K=\frac{11 \cdot N +1}{9}

    The first N that makes K an integer is N=4 and K=5
     
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  7. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    No idea. it's something they have in the philippines I guess (that's where my neice is)
     
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