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?

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Solution

Since, the tiles can't be cut.
So, the smallest common multiple,i.e., LCM of $2, 3$ and $5$ is the required shortest path.
Multiples of $2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30$
Multiples of $3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30$
Multiples of $5 = 5, 10, 15, 20, 25, 30$
Thus, $30$ is the first least number that appeared as a common multiple in the three numbers $2, 3$ and $5$
Therefore, Smallest common multiple is $30$ .
So, the shortest length of the path is $30 f e e t$ .

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