Question

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!

Answer 1

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