Tractor wheels

The front wheel of the tractor has a circumference of 18 dm and the rear 60 dm. We will make a red mark on the lowest point of both wheels. The tractor then starts. At what distance from the start will both marks appear identically at the bottom again?

Correct answer:

x =  18 m

Step-by-step explanation:

$$\begin{gathered} a=18\text{ dm } \\ b=60\text{ dm } \\ 18=2\cdot 3^2 \\ 60=2^2\cdot 3\cdot 5 \\ LCM(18,60)=2^2\cdot 3^2\cdot 5=180 \\ c=LCM(a,b)=LCM(18,60)=180\text{ dm } \\ x=c\to \text{ m}=c\mathrm{/}10\text{ m}=180\mathrm{/}10\text{ m}=18\text{ m} \end{gathered}$$

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