(1) Xiaoming's study is 2.7 meters long and 2.25 meters wide. He is going to lay a square floor tile on the floor. How many tiles does he need at least? Idea: Many square tiles can be laid in a row along the length of the study, so the side length of the square tiles used is the factor of the length of Xiaoming's study, that is, the side length of the tiles must be the common factor of the length and width of the study. In the problem, the floor tiles should be as large as possible, that is, the greatest common factor of length and width is taken as the side length, and the minimum number of tiles required is: (270 ÷ 45) × (225 ÷ 45) = 30 (blocks).
(2) A floor tile is 25cm long and 20cm wide. Now I plan to use this tile to pave a square floor. How many tiles do I need at least? The side length of a big square paved with rectangular floor tiles is a multiple of the length and width of the floor tiles. The common multiple of 25 and 20 is100,200,300, ... So as long as the side length is more than cm, a square can be used to pave this kind of floor tile. The topic requires that the paved square has the smallest side length, and the side length must be the least common multiple of the floor tile's length of 25cm and width of 20cm, 100cm, (100 ÷ 25) × (100 ÷ 20) = 20 (block). Such a floor tile needs at least.