Lay a laminate board on the floor against the architraves of your door frame.
Mark your architrave with a pen just above the top of the laminate board.
Remove the section of architrave below the mark with a handsaw. You can now slot laminate boards into the gap you've created. This will be a lot quicker and easier than cutting your boards to fit your architraves.
Measure the holes in your flooring with a tape measure including the gap at the bottom of your architraves. Remember to account for any expansion gap you need to leave as directed by the manufacturer of your flooring.
Mark a laminate board with the dimensions you've taken and then cut it to shape with a jigsaw.
Slot your cut board into place using the fitting method recommended by the manufacturer of your laminate flooring.
Place a door threshold over the expansion gap between your flooring and your door frame. Secure this into place with a silicone sealant gun.