13. The two circles in the right figure have only one common point $A$, the diameter of the larger circle is 48 cm, and the diameter of the smaller circle is 30 cm. Two beetles start from point $A$ at the same time, moving in the direction indicated by the arrows at the same speed along the two circles. Question: How many laps has the beetle on the smaller circle completed when the two beetles are farthest apart?
13. 【Solution】The distance between any two points inside a circle is farthest when measured between the endpoints of the diameter. If the beetle crawling along the smaller circle reaches point A, and the beetle crawling along the larger circle reaches point B, the distance between the two beetles is maximized. The circumference of the smaller circle is $\pi \times 30 = 30\pi$, and the circumference of the larger circle is $48\pi$, half of which is $24\pi$. The least common multiple of 30 and 24 is 120.
$$
120 \div 30 = 4 \quad 120 \div 24 = 5
$$

So, when the beetle on the smaller circle has crawled 4 laps, the beetle on the larger circle has crawled 5 half-circumferences, reaching point B. At this point, the two beetles are farthest apart.