This would be impossible as, seeing as one of the integers would be odd, the result would be an odd number.
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The three numbers added together will equal 228. The average of the three numbers will be 228 / 3 = 76. If you take one even integer from either side of 76, you get 74 and 78.Therefore, the three consecutive even integers which equal 228 are 74, 76 and 78.
The numbers are 55, and 57. Two consecutive integers have an odd sum.
The numbers are 39 and 40.
The numbers are 37 and 38.
The numbers are 97, and 99.