26
The reason is, -25 and 25 cancel each other out. -24 and 24, -23 and 23, etc. cancel each other out. In the end, you are left with 26.
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The integers are 24, 25 and 26.
25 and 26
1 and -26 is one possible answer.
The integers are 26 and 27.
If sum were 75 the integers would be 24, 25 and 26, so the next lowest sum would be 23 + 24 + 25 ie 72. The answer is thus 23.