Paving - joints

We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and in the second row in width etc. How many times will the joints meet at a distance 10 m?

Correct result:

n =  13

Solution:

$$\begin{gathered} a=18\text{ cm } \\ b=24\text{ cm } \\ l=10\text{ m}\to \text{ cm}=10\cdot 100\text{ cm}=1000\text{ cm } \\ 18=2\cdot 3^2 \\ 24=2^3\cdot 3 \\ LCM(18,24)=2^3\cdot 3^2=72 \\ x=LCM(a,b)=LCM(18,24)=72\text{ cm } \\ {n}_1=l\mathrm{/}x=1000\mathrm{/}72={\displaystyle \frac{125}{9}}\doteq 13.8889 \\ n=\lfloor n_1\rfloor =\lfloor 13.8889\rfloor =13 \end{gathered}$$

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