The Number Game

Let the first number be $x$ . Therefore the the three consecutive numbers will be $x, x+1, x+2$ .

Product of the three consecutive numbers $= x(x+1)(x+2)$

Given,

$\frac { x(x+1)(x+2) }{ x } +\frac { x(x+1)(x+2) }{ x+1 } +\frac { x(x+1)(x+2) }{ x+2 } =72\\ (x+1)(x+2)\quad +\quad x(x+2)\quad +\quad x(x+1)=72\\ 3{ x }^{ 2 }+6x-72=0\\ { x }^{ 2 }+2x-24=0$

On solving the quadratic equation, we see that $x = 4$ or $x = -6$ . But since the sum of the equation given above is positive, $x=4$ .