1989 AJHSME Problem 22

The letters \text{A}, \text{J}, \text{H}, \text{S}, \text{M}, \text{E} and the digits 1, 9, 8, 9 are "cycled" separately as follows and put together in a numbered list: \begin{array}{lccc} & & AJHSME & 1989 \\ & & & \\ 1. & & JHSMEA & 9891 \\ 2. & & HSMEAJ & 8919 \\ 3. & & SMEAJH & 9198 \\ & & ........ & \end{array}

What is the number of the line on which \text{AJHSME 1989} will appear for the first time?

\text{(A)}\ 6 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 18 \qquad \text{(E)}\ 24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.