Let 'n' be the first odd number,.
Then n+ 2 & n + 4 are the second and third odd number.
Hence
n + (n+2) + ( n + 4) = 339
Add
3n + 6 = 339
3n = 333
n = 111
n + 2 = 113
n + 4 = 115
Hence the three odd consecutive numbers are 111,113 & 115.
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The sum of two odd numbers is even and the sum of an even number and an odd number is odd.So the sum of three consecutive odd numbers is odd but 270 is even.Ergo there are no three consecutive odd numbers that sum to 270.Three consecutive numbers that sum to 270 are 89, 90, 91.Three consecutive even numbers that sum to 270 are 88, 90, 92.
The numbers are 93, 95 and 97.
Consecutive whole numbers will have an odd sum. Consecutive odd numbers, or consecutive prime numbers, will be 29 and 31.
2259 + 2261 + 2263
The average of the three numbers will have to be 29667/3 = 9889. Taking one odd number from each side means that the three odd numbers in the sum would be 9887 + 9889 + 9891 = 29667.