Find the greatest common factor of both numbers:
Factors for 150:
150: 1, 2, 5 , 6, 10, 15, 25, 30, 50, 75, 150
Factors for 270:
1, 2, 3, 5, 6 , 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The largest number they both have in common is 30, so the largest tile could be 30 cm^2.