Chicago Cubs First-Place Eliminiation Scenario
Chicago must win 18 more games (69 total) to avoid elimination from first place.
Here is a scenario in which Chicago can finish in first place with 69 wins.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        63	43	56	0.594	0.0
Cincinnati       56	50	56	0.528	7.0
St. Louis        53	52	57	0.505	9.5
Chicago          51	56	55	0.477	12.5
Pittsburgh       40	65	57	0.381	22.5

Next, we show how the remaining series of games plays out in the scenario:

Chicago wins 3 games against Cincinnati and loses 3.
Chicago wins 7 games against Milwaukee and loses 0.
Chicago wins 0 games against Pittsburgh and loses 7.
Chicago wins 7 games against St. Louis and loses 0.
Chicago wins 0 games agains teams outside the division and loses 0.

Cincinnati wins 3 games against Chicago and loses 3.
Cincinnati wins 3 games against Milwaukee and loses 0.
Cincinnati wins 0 games against Pittsburgh and loses 13.
Cincinnati wins 6 games against St. Louis and loses 0.
Cincinnati wins 0 games agains teams outside the division and loses 0.

Milwaukee wins 0 games against Chicago and loses 7.
Milwaukee wins 0 games against Cincinnati and loses 3.
Milwaukee wins 0 games against Pittsburgh and loses 6.
Milwaukee wins 5 games against St. Louis and loses 8.
Milwaukee wins 0 games agains teams outside the division and loses 0.

Pittsburgh wins 7 games against Chicago and loses 0.
Pittsburgh wins 13 games against Cincinnati and loses 0.
Pittsburgh wins 6 games against Milwaukee and loses 0.
Pittsburgh wins 3 games against St. Louis and loses 7.
Pittsburgh wins 0 games agains teams outside the division and loses 0.

St. Louis wins 0 games against Chicago and loses 7.
St. Louis wins 0 games against Cincinnati and loses 6.
St. Louis wins 8 games against Milwaukee and loses 5.
St. Louis wins 7 games against Pittsburgh and loses 3.
St. Louis wins 0 games agains teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the following final standings:
Team             W	L	PCT	GB
Chicago          69	93	0.426	0.0
Pittsburgh       69	93	0.426	0.0
Cincinnati       68	94	0.420	1.0
Milwaukee        68	94	0.420	1.0
St. Louis        68	94	0.420	1.0


Next, we explain why Chicago cannot win the division with fewer than 69 wins.

There are a total of 0 games left in the following series of games between teams in the National League Central:

For each team listed above, the table below shows the current number of wins in the (W) column.
The next column shows the maximum number of its remaining games that each team can win assuming that
ChicagoCubs finishes in first place with a total of 68 wins.

Team             W	Max Additional Wins
Total            0	0

Since the total of the Max Additional Wins column is less than 0, it is not possible for ChicagoCubs to win the division with 68 (or fewer) total wins.