Explanation:

- Let's say the three consecutive numbers are $x$, $x+1$, and $x+2$.

- Their product is $x(x+1)(x+2)$.

- When divided by each number respectively, the quotients are:

- $(x+1)(x+2)$

- $x(x+2)$

- $x(x+1)$

- The sum of these quotients is given as 74.

- So, $(x+1)(x+2)+x(x+2)+x(x+1)=74$.

- Simplify and solve the equation:

- $(x^2+3x+2)+(x^2+2x)+(x^2+x)=74$

- $3x^2+6x+2=74$

- $3x^2+6x-72=0$

- Solving, $x^2+2x-24=0$.

- Factorize:

- $(x+6)(x-4)=0$

- Hence $x=4$ (since x is positive).

- The numbers are 4, 5, 6. Their sum is 15.

- Option 2: 15 is the correct answer.

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