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Math Help - Numbers

  1. #1
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    Numbers

    Given that 132=2^2 \times 3 \times 11 and 252=2^2 \times 3^2 \times 7
    Use these results to find:

    the highest common factor of 132 and 252,

    the smallest interger k such that 132k is a multiple of 252
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  2. #2
    Senior Member Dinkydoe's Avatar
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    We have that \text{lcm}(132,252)\times \text{gcd}(132,252) = 132\times 252

    And we know that: \text{gcd}(132,252) = 2^2\times 3 = 12

    Hence \text{lcm}(132,252)/132 = k=..?
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  3. #3
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    hi what is gcd? and sorry... i didnt understand your workings
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  4. #4
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by Punch View Post
    Given that 132=2^2 \times 3 \times 11 and 252=2^2 \times 3^2 \times 7
    Use these results to find:

    the highest common factor of 132 and 252,

    the smallest interger k such that 132k is a multiple of 252
    for the hcf look at the common results you get (2^2 and 3)

    Times these together so you get 2^2*3=12

    The HCF is 12
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  5. #5
    Senior Member Mukilab's Avatar
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    Sorry I have no idea what gcd is either and I don't know of any other way to get the LCM albeit manually.
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  6. #6
    Senior Member Mukilab's Avatar
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    Just found a method for you

    Find the prime factors of both

    Then, lets say one has prime factors of (making this up) 2x2 and 3x3 and 5 and the other has prime factors of 3 and 5x5 and 7

    Now take the numbers from each one which are in most frequency. I know that sounded confusing, sorry.

    Look at it this way, the first number has more 2s than the second, so we take 2x2, the first number also has more 3s so we take 3x3 from it but the third number has more 5s and 7s so we take 5x5 and 7 from it.

    Multiply it all together and you get the HCF (2x2x3x3x5x5x7)
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  7. #7
    Senior Member Dinkydoe's Avatar
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    hi what is gcd? and sorry... i didnt understand your workings
    Sorry, thought you'd be familiar with these terms.

    gcd = greatest common divisor,
    lcm = lowest common multiple ( the one you need to find)

    There's a theorem that states gcd(n,m)* lcm(n,m)=nm. A very useful thing, since you know what value gcd(n,m) is in this case.
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  8. #8
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    Quote Originally Posted by Mukilab View Post
    Sorry I have no idea what gcd is either and I don't know of any other way to get the LCM albeit manually.
    Hello Mukilab, as for the GCD it's the greatest common divisor.

    For instance if you have 3 numbers, a,b and k. And k | a and k | b then k is a common divisor. The greatest common divisor speaks for itself then.. and its written GCD(a,b)

    I'll give you an example:

    Say we wanna find GCD(12,30) this algorithm should help you out.

    divide 30 by 12:

    30=2*12+6 <-- and add the remainder

    then divide 12 by 6:

    12=2*6+0

    meaning GCD(12,30)=6
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