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Math Help - L.c.m & h.c.f.

  1. #1
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    L.c.m & h.c.f.

    Q32: L.C.M & H.C.F. The L.C.M. (Lowest (or Least) Common Multiple) of two
    numbers is 45 times to their H.C.F (Highest Common Factor). If one of
    the numbers is 125 and sum of L.C.M. and H.C.F. is 1150, the other
    number is:
    A. 215
    B. 220
    C. 225
    D. 235

    how?
    Last edited by mr fantastic; February 11th 2011 at 01:56 AM. Reason: Re-titled.
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  2. #2
    MHF Contributor
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    The LCM is divisible by 5^3, and LCM + HCF = 2 * 5^2 * 23 is divisible by 5^2. Therefore, HCF is divisible by 5^2, which means that the second number is also divisible by 25. Of the four candidates, only 225 is divisible by 25.

    It is also possible to find the LCM and HCF of the four possible pairs and see if their sum is 1150.
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