What is the least number of equal square tiles needed to pave a floor 15 m 17 cm by 9 m 2 cm?

Problem restatement
Find the largest possible square tile size (in cm) that exactly divides both floor dimensions; then compute the number of such tiles needed.

Given data

• Length = 15 m 17 cm = 1517 cm
• Breadth = 9 m 2 cm = 902 cm

Concept/Approach
Largest square tile side = GCD of the two dimensions (in the same unit). Number of tiles = (L/gcd) × (B/gcd).

Step-by-Step calculation
GCD(1517, 902): 1517 − 902 = 615; 902 − 615 = 287; 615 − 2×287 = 41; 287 − 7×41 = 0 ⇒ gcd = 41 cmTiles along length = 1517 / 41 = 37Tiles along breadth = 902 / 41 = 22Total tiles = 37 × 22 = 814

Verification/Alternative
41 cm divides both lengths exactly; any larger square would fail to tile one dimension evenly.

Common pitfalls
Leaving dimensions in mixed metres–centimetres or using LCM instead of GCD.

Final Answer
814