The numbers are 65, 66, and 67..
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48, 49, 50, 51
There is no set of three consecutive integers whose sum is 71.
The sum of three consecutive integers is -72
There must be three consecutive integers to guarantee that the product will be divisible by 6. For the "Product of three consecutive integers..." see the Related Question below.
That isn't possible. The three consecutive number are assumed to be integers; the sum of three consecutive integers is always a multiple of 3 (try it out).