You are using a 12V supply, 1 resistor, and 4 LEDs. Each LED takes 2.4V across them so that makes 4*2.4=9.6V. That means 2.4V will be across the resistor. By using I=V/R=2.4V/27ohms you get aproximately 89mA. Your LEDs take 80-100mA of forward current to turn them on. By using P=VI, you get 89mA*2.4V=0.2136W. A 1/4W resistor can still be used, but it's safer to go with a 1/2W resistor.
It should be ok to use a 1/2W 27ohm resistor and 4 LEDs for your circuit.
so 12v divided by 5 is 2.4. Which is exactly what they use. Im still going to throw a small resistor on the series to compensate for fluctuations in power.