Least number of square tiles: How many least number of equal square tiles are required to pave a floor 15.17 m by 9.02 m?

Introduction / Context:
To minimize the number of equal square tiles, use the largest possible square tile whose side length equals the greatest common divisor (GCD) of the floor dimensions (expressed in the same unit).

Given Data / Assumptions:

• Dimensions: 15.17 m and 9.02 m
• Convert to cm to use integers: 1517 cm and 902 cm
• Tile side = GCD(1517, 902) cm

Concept / Approach:
Number of tiles = (Area of floor) / (Area of one tile) = (L * B) / (g^2), where g = GCD(L, B) in the same unit.

Step-by-Step Solution:

Verification / Alternative check:
41 cm = 0.41 m. Floor in tiles: (15.17/0.41) * (9.02/0.41) = 37 * 22 = 814, consistent.

Why Other Options Are Wrong:
714, 614, 713, 902 arise from incorrect GCD or rounding; 814 is minimal and exact.

Common Pitfalls:
Using LCM, or choosing a smaller non-maximal tile side leading to more tiles, or mixing metres and centimetres.

Final Answer:
814