Lamps on playground

The playground has the shape of a rectangle of 36 x 50m. After how many meters can place the lamps on its lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps?

Final Answer:

x =  2 m

Step-by-step explanation:

$$\begin{gathered} a=36\text{m}\to \text{cm}=36\cdot 100\text{cm}=3600\text{cm} \\ b=50\text{m}\to \text{cm}=50\cdot 100\text{cm}=5000\text{cm} \\ 3600=2^4\cdot 3^2\cdot 5^2 \\ 5000=2^3\cdot 5^4 \\ \text{GCD}(3600,5000)=2^3\cdot 5^2=200 \\ {x}_1=GCD(a,b)=GCD(3600,5000)=200\text{cm} \\ x=x_1\to \text{m}=x_1:100\text{m}=200:100\text{m}=2\text{m}=2\text{m} \end{gathered}$$

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