Least Common Multiple

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:

$$ \begin{array}{|l} \llap{2~~~~} 72,108 \\ \hline \llap{2~~~~} 36,54 \\ \hline \llap{3~~~~} 18,27\\ \hline \llap{3~~~~} 6,9 \\ \hline \phantom{x}2,3 \end{array} $$ $$ \textup{L.C.M. }=2×2×3×3×2×3$$ $$ \textup{L.C.M. }=216$$