Two gears

Two gears with 13 and 7 teeth rotate locked into each other. How many turns does a big wheel have to make for both wheels to be in the starting position again?

Correct answer:

x =  7

Step-by-step explanation:

$$\begin{gathered} 13\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ 7\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ LCM(13,7)=7\cdot 13=91 \\ s=LCM(13,7)=91 \\ x=s\mathrm{/}13=91\mathrm{/}13=7 \end{gathered}$$

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