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The least common multiple of two numbers is 84, and one of the numbers is 5 less than other number. What are the numbers? Complete the explanation ( The two numbers are ___ and ___. 84 is a multiple of each of its factors. The factors with a difference of 5 are ___ and ___, and their LCM is 84. Please help me!

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tramserran

factor 1 = x

factor 2 = x - 5

(factor 1)  *  (factor 2)  = 84

     (x)      *      (x - 5)     = 84

           x² - 5x              = 84

               x² - 5x - 84   = 0

              (x - 12) (x + 7)  = 0

x - 12 = 0    or     x + 7 = 0

  x = 12       or      x = -7

factor 2 = x - 5   = (12) - 5  = 7    or    (-7) - 5  =  -12

Answer: 12, 7     or    -7, -12

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