Five bottling machines fill 240 bottles in 20 minutes, 120 bottles in 15 minutes, 180 bottles in 10 minutes, 200 bottles in 10 minutes and 90 bottles in 6 minutes, respectively. If they work for an hour and a half, how many bottles will the fastest bottler fill?

First, we need to find the rate at which each machine fills bottles per minute. To do this, we divide the number of bottles filled by the time taken:

Machine 1: 240 bottles in 20 minutes = \frac{240}{20}=12 bottles/minute \
Machine 2: 120 bottles in 15 minutes = \frac{120}{15}=8 bottles/minute \
Machine 3: 180 bottles in 10 minutes = \frac{180}{10}=18 bottles/minute \
Machine 4: 200 bottles in 10 minutes = \frac{200}{10}=20 bottles/minute \
Machine 5: 90 bottles in 6 minutes = \frac{90}{6}=15 bottles/minute \

Now, we need to find how many bottles each machine will fill in an hour and a half (90 minutes):

Machine 1: 12 \times 90 = 1080 bottles \
Machine 2: 8 \times 90 = 720 bottles \
Machine 3: 18 \times 90 = 1620 bottles \
Machine 4: 20 \times 90 = 1800 bottles \
Machine 5: 15 \times 90 = 1350 bottles \

The fastest bottler, machine 4, will fill \boxed{1800} bottles.

\textbf{Answer: 1800 bottles}