right now, the Cubs magic number is 10. It decreases one game every time the Cubs win, /or every time the Cardinals lose. the formula is 163 (the regular season plus one) - minus first place teams wins - minus second place teams losses.
the earliest they can clinch if, with out the help of the Cardinals losing, would be next Wednesday, when the Cubs are in St. Lois against the Cardinals. When you play against that team, it's an automatic two game swing.
If the Cubs win the next five, and the Cardinals lose the next five, they can clinch it in Houston on Sunday against the Astros.
But, I think they'll clinch it at home after the Cardinals series. It'll be under five games then to clinch the division, and they have a long home stand against the Brewers, Red, and Cardinals. and they've dominated against the Brewers and Reds this year.