12. (3 points) Two natural numbers $a$ and $b$, their least common multiple is 60. Then, the difference between these two natural numbers has $\qquad$ possible numerical values.
12. (3 points) Two natural numbers $a$ and $b$, their least common multiple is 60. Then, the difference between these two natural numbers has $\qquad$ possible values.

【Solution】Solution: If the order of $a, b$ is not considered, there should be 23 cases.
$$
\begin{array}{l}
(1,60),(2,60),(3,20),(3,60),(4,15),(4,30),(4,60),(5,12),(5, \\
60),(6,20),(6,60), \\
(10,12),(10,60),(12,15),(12,20),(12,30),(12,60), \\
(15,20),(15,60),(20,30),(20,60),(30,60),(60,60)
\end{array}
$$

Their differences are $0,2,3,5,7,8,10,11,14,17,18,26,30,40,45,48,50,54$, $55,56,57,58,59$; there are 23 differences in total;

Therefore, the answer is: 23.