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29 July, 03:38

3) The sum and the difference of the LCM and GCD of two numbers are 312 and 264 respectively. Find the numbers if their sum is 168.

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  1. 29 July, 07:35
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    The numbers are 72 and 96.

    Step-by-step explanation:

    LCM + GCF = 312

    LCM - GCF = 264

    2*LCM = 576

    LCM = 576/2 = 288

    HCF = 312-288 = 24

    The product of two numbers = HCF*LCM

    Let the numbers be x and (168-x)

    x (168-x) = 24*288 = 6912

    x^2-168x+6912 = 0

    x = [168 + (168^2 - 4*6912) ^0.5]/2

    = [168 + (28224-27648) ^0.5]/2

    = [168 + 576^0.5]/2

    = (168+24}/2

    = 192/2

    = 96 and the other number is 168-96 = 72.
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