The first year after 1999 which is the product of three consecutive integers is:

Question

2004
2040
2046
2052
2184
Please show working out and choose either one of these years

Answer 1

Let the first integer is (x-1) then the 2nd is x, and the 3rd is (x+1)
The product is (x-1)x(x+1)=(x^2-1)x=
x^3-x. If x=13 then x^3-x=13^3-13=
2197-13=2184. (12^3=1728)

Answer 2

2184