# Will concatenation always works?

Dr. Frankenthree creates numbers by splicing three consecutive positive integers together. He notices these numbers are multiples of 3:

\begin{align} {\color{blue}7}{\color{red}8}{\color{green}9} &= 3 \times 263 \\ {\color{blue}14}{\color{red}15}{\color{green}16} &= 3 \times 47172 \\ {\color{blue}50} {\color{red}51}{\color{green}52} &= 3 \times 168384 \\ {\color{blue}198} {\color{red}199}{\color{green}200} &= 3 \times 66066400. \end{align}

Are the numbers Dr. Frankenthree creates in this way always multiples of 3?

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