In order to find the least common multiple (LCM) of these three numbers, first let's factorate them:
[tex]\begin{gathered} 30\to2\cdot3\cdot5 \\ 20\to2\cdot2\cdot5 \\ 50\to2\cdot5\cdot5 \end{gathered}[/tex]The LCM will be the product of each factor in the maximum amount of time they appear.
So we have:
[tex]\text{LCM}=2\cdot2\cdot3\cdot5\cdot5=300[/tex]So the LCM is 300.