Question

There is a garden in Anu’s house. In the middle of the garden there is a path. They decided to tile the path using tiles of length 2 feet, 3 feet and 5 feet.

The mason tiled the first row with 2 feet tiles, the second row with 3 feet tiles and the third row with 5 feet tiles. The mason has not cut any of the tiles. Then what is the shortest length of the path?

Answer 1

The smallest common multiple of 2, 3, and 5 is the shortest length of the path.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 17, 18, 20, 22, 24, 26, 28, 30

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 5: 5, 10, 15, 20, 25, 30

The smallest common multiple is 30.

So, the shortest length of the path is 30 m.