# Will concatenation always works?

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

\begin{aligned} {\color{#3D99F6}7}{\color{#D61F06}8}{\color{#20A900}9} &= 3 \times 263 \\ {\color{#3D99F6}14}{\color{#D61F06}15}{\color{#20A900}16} &= 3 \times 47172 \\ {\color{#3D99F6}50} {\color{#D61F06}51}{\color{#20A900}52} &= 3 \times 168384 \\ {\color{#3D99F6}198} {\color{#D61F06}199}{\color{#20A900}200} &= 3 \times 66066400. \end{aligned}

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

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