1. **State the problem:** We need to find three consecutive integers whose sum is 57. 2. **Define variables:** Let the first integer be $x$. Then the next two consecutive integers are $x+1$ and $x+2$. 3. **Write the equation:** The sum of these three integers is given by: $$x + (x+1) + (x+2) = 57$$ 4. **Simplify the equation:** $$x + x + 1 + x + 2 = 57$$ $$3x + 3 = 57$$ 5. **Isolate $x$:** $$3x + 3 = 57$$ $$3x = 57 - 3$$ $$3x = 54$$ 6. **Divide both sides by 3:** $$\cancel{3}x = \cancel{3}18$$ $$x = 18$$ 7. **Find the three integers:** The integers are $18$, $19$, and $20$. 8. **Check the sum:** $$18 + 19 + 20 = 57$$ which is correct. **Final answer:** The three consecutive integers are $18$, $19$, and $20$.