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

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#### Solution

It is given that:

Length of a tile = 15m 17m = 1517cm [β΅ 1m = 100cm]

Breadth of a tile = 9m 2m = 902cm

∴ Side of each square tile = HCF (1517, 902)

Prime factorization:

1517 = 37 × 41

902 = 22 × 41

∴ HCF = product of smallest power of each common prime factor in the numbers = 41

∴ Required number of tiles = `"π΄πππ ππ πππππππ" / "π΄πππ ππ πππ π‘πππ" `=` (1517 × 902) / (41 × 41 )= 37 × 22 = 814`

Concept: Euclidβs Division Lemma

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