The least common multiple can be used to find the smallest square formed by equal sized shapes
The least number of tiles to be used is 15 tiles
The arrangement of the tiles, with the 6 inch side as base is 3 rows by 6 columns of tiles
The reason the above responses are correct is as follows:
The unit area of each square tile = 6 inches by 10 inches
Therefore, the area of the square obtained is a factor of 6 × 10 = 60 in.²
The side of the square have 6 and 10 as factors
The lowest common multiple of 6 and 10 is 30
Therefore, the smallest square has a side length of 30 inches and an area of 30 in. × 30 in. = 900 in.²
The least number of tiles = Area/(The area of each tile)
Therefore, the least number of tiles = 900 in.²/(60 in.²/tile) = 15 tiles
The least number of tiles = 15 tiles
The arrangement of the 15 tiles are as follows;
With the 6 inch width side as the base, five tiles are arranged along the base, three more rows are constructed using the same process to form the 30 inch by 30 inch square to give 3 rows by 6 columns of tiles
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