Find the least number of square tiles required to pave the ceiling of a room 15 m 17 cm long and 9 m 2 cm broad.

We know 1m = 100cm.

So,

15m 17cm = 1500 + 17 = 1517cm

And 9m 2cm = 900 + 2 = 902 cm

Least number of square tiles required to pave the ceiling of this area if largest tiles are used.

Length of largest tile = H.C.F. of 1517 cm and 902 cm

Prime factors of 1517 and 902 -

1517 = 41 × 37

902 = 2 × 11 × 41

So HCF = 41

∴ Area of tiles of largest length and width = (41 × 41) cm²

And area of room = length × width = (1517 × 902) cm²

So minimum number of tiles required = (1517 × 902) cm²/ (41 × 41) cm² = 814.