Square tiles paving a floor

CMAT 2021 · Quantitative Techniques & Data Interpretation · Easy · HCF and LCM

The dimensions of a floor are 18×2418 \times 24. What is the smallest number of identical square tiles that pave the entire floor without the need to break any tile?

  1. A.

    6

  2. B.

    24

  3. C.

    8

  4. D.

    12

Answer

D

Explanation

To minimize the number of square tiles, we must maximize the side length of each tile. Side length of tile = HCF(18,24)=6\text{HCF}(18, 24) = 6.

Number of tiles required = Area of floorArea of 1 tile=18×246×6=3×4=12\frac{\text{Area of floor}}{\text{Area of 1 tile}} = \frac{18 \times 24}{6 \times 6} = 3 \times 4 = 12.

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