$36 \cdot 13$ letters $A, J, H, S, M, E$ and numbers $1,9,8,9$ are "rotated" as follows:
\begin{tabular}{rrr} 
AJHSME & 1989 & \\
1. JHSMEA & 9891 & (1st rotation) \\
2. HSMEAJ & 8919 & (2nd rotation) \\
3. SMEAJH & 9198 & (3rd rotation) \\
..... & &
\end{tabular}

To make AJHSME1989 reappear, the minimum number of rotations required is
(A) 6.
(B) 10.
(C) 12.
(D) 18.
(E) 24.
(5th American Junior High School Mathematics Examination, 1989)
[Solution] The letters $A, J, H, S, M, E$ return to their original positions after "rotating" 6 times;
the numbers $1,9,8,9$ return to their original positions after "rotating" 4 times.
Therefore, to make AJHSME 1989 return to its original state, it needs to rotate at least $[4,6]=12$ times, where $[a, b]$ represents the least common multiple of integers $a, b$.
Thus, the answer is $(C)$.