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Verified Answer :

Well 88 + 89 + 90 = 267. So the largest integer is 90.

If we cal lthe first number 'n' then we know that the numbers are n, n+1 and n+2 and we know the sum:
\(n+(n+1)+(n+2)=267\)
therefore:
\(3n+3=267\)
\(3n=264\)
\(n=88\)

The numbers are 88,89,90, the largest of which is 90.

To check: 88+89+90=267. Checks.