Question

What is LCM of 18,24,36,45

Answer 1

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

`\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{18 \ \ \ 24 \ \ \ 36 \ \ \ 45 }\\ \ 9 \ \ \ 12 \ \ \ 18 \ \ \ 45\\ \ 9 \ \ \ \ \ 6 \ \ \ \ \ 9 \ \ \ 45\\ \ 9 \ \ \ \ \ 3 \ \ \ \ \ 9 \ \ \ 45\\ \ 3 \ \ \ \ \ 1 \ \ \ \ \ 3 \ \ \ 15\\ \ 1 \ \ \ \ \ 1 \ \ \ \ \ 1 \ \ \ \ 5\\ \ 1 \ \ \ \ \ 1 \ \ \ \ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 5\\ \: \end{matrix} \end{gathered}$}`

`\sf{L.c.m.(18,24,36,45)=2*2*2*3*3*5 }`

`\sf{L.c.m.(18,24,36,45)=2^(3) *3^(2) *5 }`

`\boxed{\boxed{\sf{L.c.m.(18,24,36,45)=360 }}}`

Therefore, the least common multiple of 18, 24, 36 and 45 is 360.