Della has a box of ping-pong balls. No matter she counts the balls $8$ by $8$, $10$ by $10$, or $12$ by $12$, there are always $3$ balls left. How many ping-pong balls are there in the box at least? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
If the ping pong balls in the box are reduced by $3$, then there will be no extra balls when you count them $8$ by $8$, $10$ by $10$, or $12$ by $12$. It means that the number of the ping pong balls is a common multiple of $8$, $10$, and $12$ after being reduced by $3$. If you want to know how many ping pong balls there are at least, you can first find the least common multiple of $8$, $10$ and $12$, and then add $3$ to get the answer.  $$\begin{array}{l} {2\left\textbar{} \underline{\textasciitilde8\textasciitilde\textasciitilde10\textasciitilde\textasciitilde12}\right. }\textbackslash\textbackslash{\textasciitilde2\left\textbar{} \underline{4\textasciitilde\textasciitilde\textasciitilde5\textasciitilde\textasciitilde\textasciitilde6}\right. }\textbackslash\textbackslash{\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde2\textasciitilde\textasciitilde\textasciitilde5\textasciitilde\textasciitilde\textasciitilde3} \end{array}$$  $2\times2\times2\times5\times3=120$  $120+3=123$ 