Square tile space

What is the smallest square space we can tile with tiles measuring 25 x 15 cm, knowing there will be no need to cut them? How many tiles will we use?

Final Answer:

a =  0.75 m
S =  0.5625 m²
n =  15

Step-by-step explanation:

$$\begin{gathered} x=25\text{cm} \\ y=15\text{cm} \\ 25=5^2 \\ 15=3\cdot 5 \\ LCM(25,15)=3\cdot 5^2=75 \\ z=LCM(x,y)=LCM(25,15)=75\text{cm} \\ a=z\to \text{m}=z:100\text{m}=75:100\text{m}=0.75\text{m}=0.75\text{m} \end{gathered}$$

$S=a^2=0.75^2=0.5625{\text{m}}^2$

$n=(z/x)\cdot (z/y)=(75/25)\cdot (75/15)=15$

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