Question

The least common multiple of two numbers is 60, and one of the numbers is 7 less than the other number. What are the numbers? Explain your answer.

Answer 1

Two numbers (integer only): 5 , 12

Explanation:

Suppose two numbers are integers: ax and ay, a is common factor and x,y no more common factor

axy = 60 a: 1,2,3,4,6,10,12,30

ax - ay = a(x-y) = 7

after test , I exclude 3,4,6,10,12,30

if a=1 xy=60 (x,y): (3,10) (4,15) (5,12)

(5,12): LCM: 5*12=60 12-5=7

if a=2 xy=30 (x,y): (2,15) (3,10) (5,6) No solution in this combination