11. A wooden stick of length $L$, is divided into 8, 12, and 18 equal segments using red, blue, and black lines respectively. The stick is then cut at each division line. How many segments will be obtained in total? What is the length of the shortest segment?
【Analysis】To meet the conditions, $L$ must be a multiple of 8, 12, and 18, so we first find the least common multiple of these three numbers, and the least common multiples of each pair, to determine the overlapping segments, and then solve using the principle of inclusion-exclusion.

【Solution】Assume $L=[8,12,18]=72$ times $K$, i.e., $L=72K$. Then: the red line divides the stick into 8 equal parts (9 division points), each part being $9K$ in length;

the blue line divides the stick into 12 equal parts (13 division points), each part being $6K$ in length;
the black line divides the stick into 18 equal parts (19 division points), each part being $4K$ in length;
Also, $[9K, 6K]=18K$, overlapping 4 segments; $[6K, 4K]=12K$, overlapping 6 segments; $[9K, 4K]=36K$, overlapping 2 segments;
$[9K, 6K, 4K]=36K$, overlapping 2 segments.
By the principle of inclusion-exclusion, the total number of segments is: $(8+12+18)-4-6-2+2=28$ (segments);
or the total number of points is: $(9+13+19)-5-7-3+3=29$ (division points), so there are 28 segments in total.
Thus, the shortest segment is the distance between the red line and the black line: $L \div 72=\frac{L}{72}$.