Floor tiling – Least number of square tiles (HCF approach):\nA room 5 m 44 cm long and 3 m 74 cm broad is to be paved with identical square tiles. Find the least number of square tiles required (use consistent units).

Introduction / Context:
To minimise the number of square tiles covering a rectangle without cutting, choose the largest possible tile that exactly divides both dimensions, i.e., the HCF of the side lengths (in the same unit).

Given Data / Assumptions:

• Length = 5 m 44 cm = 544 cm.
• Breadth = 3 m 74 cm = 374 cm.

Concept / Approach:
Tile side = HCF(544, 374). Number of tiles = (544 × 374) / (HCF^2).

Step-by-Step Solution:

Verification / Alternative check:
Try any larger tile side (>34 cm): it will not divide at least one dimension; using smaller sides increases count.

Why Other Options Are Wrong:
136, 146, 166 arise from incorrect HCF or arithmetic; 176 is exact.

Common Pitfalls:
Not converting metres to centimetres consistently; computing LCM instead of HCF; arithmetic slips.

Final Answer:
176