## Task 2 - 070622

Each of the two front wheels of a vehicle has a circumference of $210 \mathrm{~cm}$, and each of the two rear wheels has a circumference of $330 \mathrm{~cm}$.

Determine the shortest distance (in $\mathrm{m}$) that the vehicle must travel on a straight, flat road so that each of its wheels has completed an exact number of revolutions!
To fulfill the conditions of the task, the vehicle must cover a distance whose length is a common multiple, and specifically the least common multiple, of $210 \mathrm{~cm}$ and $330 \mathrm{~cm}$. Therefore, we determine the $\mathrm{lcm}$ of 210 and 330:

$$
\begin{aligned}
210 & =2 \cdot 3 \cdot 5 \cdot 7 \\
330 & =2 \cdot 3 \cdot 5 \cdot 11 \\
l c m & =2 \cdot 3 \cdot 5 \cdot 7 \cdot 11=2310
\end{aligned}
$$

The shortest distance that the vehicle must cover so that each wheel completes an exact number of revolutions is therefore $2310 \mathrm{~cm}=23.10 \mathrm{~m}$ long.

Verification:

$2310: 210=11$ and $2310: 330=7$. The front wheels make exactly 11 revolutions, and the rear wheels make exactly 7 revolutions.