Hopefully, your apartment is currently free of pests. But if you see a mouse scamper across the floor when you turn on the light in the laundry room, or if you notice a large cockroach sitting in the lobby, this should concern you. What's in your building's common areas today could be in your apartment tomorrow, which means your good efforts at keeping your apartment pest-free may be threatened.
Since common areas are spaces that you share with other tenants in the building and that the landlord controls, you can't start setting glue traps or spraying pesticides. If you spot a pest problem, promptly bring it to your landlord's attention. Keep a log that shows what you saw and when. If your landlord isn't responsive, follow up with another call, get several tenants to sign a letter, or, if your building has a tenants' association, bring up the issue at the association's next meeting.