Since we are looking for a sum, we add. Since we know the integers are consecutive, then we know that the second number will be one more than the first number and the third number will be two more than the first number... so we can set up the equation by setting the first number as "x" and then
x + (x + 1) + (x + 2) = 1623
Now we combine like terms
3x + 3 = 1623
Subtract 3 from each side
3x = 1620
Divide each side by 3
x = 1620/3 = 540
So we have the first number as 540, so the next numbers will be 541 (x +1) and 542 (x + 2)
540, 541, and 542
Check the answer by adding them together to see if they add to 1623
