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8 and 9
Consecutive numbers are whole numbers whose difference is 1.
Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.
There is no set of 3 consecutive odd numbers whose product is 6,873. However, there is a set of 3 consecutive odd numbers whose sum is 6,873: 2289, 2291, and 2293.
The numbers are 64 and 65.