Problem 3. Given is a rectangle with side lengths $2023 \mathrm{~cm}$ and $1309 \mathrm{~cm}$. The rectangle is divided into equal squares with the largest possible side length expressed in centimeters as a natural number. Determine the sum of the perimeters of the divided squares.
Solution. Clearly, the length of the side a of the divided squares must be a divisor of 2023 and 1309. However, the length of the side a needs to be as large as possible, so $a=\operatorname{GCD}(2023,1309)=119 \mathrm{~cm}$. Furthermore, 2023:119 =17 and 1309:119=11, which means the rectangle is divided into $17 \cdot 11=187$ squares with side $a=119 \mathrm{~cm}$. Finally, the sum of the perimeters of the divided squares is $L=187 \cdot 4 a=187 \cdot 4 \cdot 119=89012 \mathrm{~cm}$.