Let the numbers be chosen as (n-1), n and (n+1).
Then the sum of their resulting quotients when their product is divided by each of them is:
n(n+1) + (n+1)(n-1) + n(n-1)
which is equal to 74.
Therefore, we have:
n(n+1) + (n+1)(n-1) + n(n-1) = 74
Which on simplification gives:
(n)^2 = 25 which implies n = (-5) or n = (+5)
Thus, the three consecutive numbers are: (-6,-5,-4) or (4,5,6).

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