Image arrangement

Our task is to save the rectangular images with dimensions of 105 mm and 42 mm so that we cover the smallest square. What will be its size, and how many pictures do we need?

Final Answer:

a =  210 mm
n =  10

Step-by-step explanation:

$$\begin{gathered} 105=3\cdot 5\cdot 7 \\ 42=2\cdot 3\cdot 7 \\ LCM(105,42)=2\cdot 3\cdot 5\cdot 7=210 \\ a=LCM(105,42)=210\text{mm} \end{gathered}$$

$$\begin{gathered} S_1=a^2=210^2=44100 \\ {S}_2=105\cdot 42=4410 \\ n=S_1/S_2=44100/4410=10 \end{gathered}$$

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