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Let's called the first integer x. The second would be x+1 and the third x+2. Adding all these integers together would result in 114:

x+(x+1)+(x+2)=114

x+x+1+x+2=114

3x+3=114

Subtract 3 from both sides:

3x=111

Divide both sides by 3:

x=37

The first number is 37, so the three numbers are 37, 38, and 39.

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