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Find the Least Number of Square Tiles Required to Pave the Ceiling of a Room 15m 17cm Long and 9m 2cm Broad. - Mathematics

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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      [∡ 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΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝑐𝑒𝑖𝑙𝑖𝑛𝑔" / "π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘œπ‘›π‘’ 𝑑𝑖𝑙𝑒" `=` (1517 × 902) / (41 × 41 )= 37 × 22 = 814`

Concept: Euclid’s Division Lemma
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