Two natural numbers $\mathrm{a}, \mathrm{b}$ have a least common multiple equal to 50. How many possible values of $\mathrm{a}+\mathrm{b}$ are there?
4. Answer: 8

Analysis: Since: $50=2 \times 5^{2}, \mathrm{a}, \mathrm{b}$ are divisors of 50, they can only take 1, 2, 5, 10, 25, 50. Assuming $a \geqslant b$, when $a=50$, $b=1, 2, 5, 10, 25, 50$; when $a=25$, $b=2, 10$. 
Therefore, $\mathrm{a}+\mathrm{b}$ has 8 different possible values.
For two natural numbers $a, b$ whose least common multiple is 50, when $a \geqslant b$, the different values of $a+b$ can be listed as follows:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline$a$ & 50 & 50 & 50 & 50 & 50 & 50 & 25 & 25 \\
\hline$b$ & 1 & 2 & 5 & 10 & 25 & 50 & 2 & 10 \\
\hline$a+b$ & 51 & 52 & 55 & 60 & 75 & 100 & 27 & 35 \\
\hline
\end{tabular}