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Math Help - Good number theroy question

  1. #1
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    Good number theroy question

    Here was a very tough bonus question we had on our pre-calc final today

    (x^3*y^3*z^3)/(gcf(x,y)*gcf(x,z)*gcf(y,z)*lcm(x,y)*lcm(x,z)*lcm( y,z))=(lcm(x,y)*lcm(x,z)*lcm(y,z))/(gcf(x,y,z))

    sorry i dont know latex very well, but its two things set equal and watch out for the division signs

    greatest common factor =gcf, so like gcf(2,4)=2. least common multiple = lcm, so lcm(2,3)=6

    where x>y>z. Find the smallest possible value of x that satisfies this equation.

    I experiemented with numbers and I guessed 150(i tried splitting up into its factors and creating other numbers from them)...i wasnt sure though. can anyone verify because I do not want to wait until next Friday to see what mny final grade might have been.

    Thye choices were like 50, 60, 90, 150, or 180

    Thanks
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  2. #2
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    It's not on the list, but I would choose x = 36 (with y = 12 and z = 6). I think that gives a correct result.
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  3. #3
    Moo
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    Note that you can simplify the LHS to xyz
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