Example 1:
$$ \textup{Find the L.C.M. of } 24 \textup{ and } 42 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 30,66 \\ \hline
\llap{3~~~~} 15,33 \\ \hline
\phantom{x}5,11
\end{array}
$$
$$ \textup{L.C.M. }=2×3×5×11$$
$$ \textup{L.C.M. }=330$$
Example 2:
$$ \textup{Find the L.C.M. of } 45 \textup{ and } 15 $$
Solution:
$$
\begin{array}{|l}
\llap{3~~~~} 45,15\\ \hline
\llap{5~~~~} 15,5\\ \hline
\phantom{x}3,1
\end{array}
$$
$$ \textup{L.C.M. }=3×5×3$$
$$ \textup{L.C.M. }=45$$
Example 1:
$$ \textup{Find the L.C.M. of } 60 \textup{ and } 90 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 60,90 \\ \hline
\llap{3~~~~} 30,45 \\ \hline
\llap{5~~~~} 10,15 \\ \hline
\phantom{x}2,3
\end{array}
$$
$$ \textup{L.C.M. }=2×3×5×2×3$$
$$ \textup{L.C.M. }=180$$
Example 2:
$$ \textup{Find the L.C.M. of } 735 \textup{ and } 980 $$
Solution:
$$
\begin{array}{|l}
\llap{5~~~~} 735,980 \\ \hline
\llap{7~~~~} 147,196 \\ \hline
\llap{7~~~~} 21,28 \\ \hline
\phantom{x}3,4
\end{array}
$$
$$ \textup{L.C.M. }=5×7×7×3×4$$
$$ \textup{L.C.M. }=2940$$
Example 1:
$$ \textup{Find the L.C.M. of } 120 \textup{ and } 180 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 120,180 \\ \hline
\llap{2~~~~} 60,90 \\ \hline
\llap{3~~~~} 30,45 \\ \hline
\llap{5~~~~} 10,15 \\ \hline
\phantom{x}2,3
\end{array}
$$
$$ \textup{L.C.M. }=2×2×3×5×2×3$$
$$ \textup{L.C.M. }=360$$
Example 2:
$$ \textup{Find the L.C.M. of } 72 \textup{ and } 108$$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 72,108 \\ \hline
\llap{2~~~~} 36,54 \\ \hline
\llap{3~~~~} 18,27\\ \hline
\llap{3~~~~} 6,9 \\ \hline
\phantom{x}2,3
\end{array}
$$
$$ \textup{L.C.M. }=2×2×3×3×2×3$$
$$ \textup{L.C.M. }=216$$