If it's the bottom bracket, both crankarms will feel loose.

Loosness in just the left crankarm is a frequent issue. If you're finding that it's important to immediately tighten the bolt that holds it. If you wait too long you will damage the crank arms interface with the bottom bracket and you'll have to acquire a replacement crank arm. The torque spec for that bolt is usually about 30 lb/ft. That's quite a bit. If you are trying to tighten that bolt with an Allen wrench that's only about 100 mm long, you aren't going to get to 30 lb/ft.