Cyanoacrylate super glues do not work on PLA. Epoxies are a hassle, take a long time to set, and not as strong as the rest of your printed part. Hot air tools melt too much material, make good joints very difficult to acheive, and cannot fill gaps.
For a strong, long lasting joint weld pieces together with a soldering iron using this rod as filler material.
Run your extruder as high as it will go and move the bed out of the way (position over a dump location). Extrude 5 or 6 inches (12-15 cm) of filament (this is ussually called "purge" on your host software, you will only need to purge a few mm of 3 mm filiment to get the desired length of extruded filament. Blow on the filament to cool it (if you don't have a fan) and pull it off of the extruder. Repeat a dozen or so times.
The next time you need to join PLA, find an old cheap soldering iron or a worn out tip for your good one. I used a cheap radio shack verion on "high" (40W) with a blunt damaged tip that can no longer be used for soldering. Place a piece of rod along the joint. Run over the joint with the soldering iron melting the rod and a small amount of both pieces to be be joined. For joints with large gaps, repeat with more filler rod.
This method forms joints as strong or stronger than the printed part, fills gaps, and gives great control over how much material is melted.