Let N be the first integer, then N+1 is the second integer and N+2 is the third
integer. To find their sum you write them down with + signs between them,
like this:

N + N+1 + N+2

You are told this sum is 252. so you write = 252 after that and you have:

N + N+1 + N+2 = 252

Now you combine like terms on the left side:

3N + 3 = 252

Now you subtract 3 from both sides

3N = 249

Now you divide both sides by 3 and get

N = 83

That's the first integer.
Now to find the second integer you add one to it

Second integer = 84

To find the third, which is the largest integer you add one to
that and get

Third integer = 85

The consecutive integers are 83,84,85

As a check, add them up and. sure enough, you do get 252

The problem asks for the largest one so the answer is 85

Edwin