Planetary system

Robert has built a mechanical model solar system with three balls representing planets at the end of rods. Each rod is attached to the center, representing the Sun. The planets are lined up when he turns on the motor. The innermost planet makes a revolution in 16 seconds, the middle planet makes a revolution in 28 seconds, and the outermost planet makes a revolution in 40 seconds. After how many seconds will the planets be lined up again?

Correct answer:

T =  560 s

Step-by-step explanation:

$$\begin{gathered} 16=2^4 \\ 28=2^2\cdot 7 \\ 40=2^3\cdot 5 \\ LCM(16,28,40)=2^4\cdot 5\cdot 7=560 \\ T=LCM(16,28,40)=560\text{s} \end{gathered}$$

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