Respuesta :
To obtain the least common multiple (l.c.m), we will do it by canonical decomposition or simultaneous decomposition.
This method consists of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{18 \ \ \ 24 \ \ \ 36 \ \ \ 45 }\\ \ 9 \ \ \ 12 \ \ \ 18 \ \ \ 45\\ \ 9 \ \ \ \ \ 6 \ \ \ \ \ 9 \ \ \ 45\\ \ 9 \ \ \ \ \ 3 \ \ \ \ \ 9 \ \ \ 45\\ \ 3 \ \ \ \ \ 1 \ \ \ \ \ 3 \ \ \ 15\\ \ 1 \ \ \ \ \ 1 \ \ \ \ \ 1 \ \ \ \ 5\\ \ 1 \ \ \ \ \ 1 \ \ \ \ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 5\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\sf{L.c.m.(18,24,36,45)=2\times2\times2\times3\times3\times5 }[/tex]
[tex]\sf{L.c.m.(18,24,36,45)=2^{3} \times3^{2} \times5 }[/tex]
[tex]\boxed{\boxed{\sf{L.c.m.(18,24,36,45)=360 }}}[/tex]
Therefore, the least common multiple of 18, 24, 36 and 45 is 360.
