Question

LCM OF 32, 42 ,48

30 , 42

Answer 1

To obtain the least common multiple of (l.c.m) we must do it in simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

`\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{32 \ \ \ 42 \ \ \ 48}\\ 16 \ \ \ 21 \ \ \ 24\\ \ 8 \ \ \ 21 \ \ \ 12\\ \ 4 \ \ \ 21 \ \ \ \ 6\\ \ 2 \ \ \ 21 \ \ \ \ 3\\ \ 1 \ \ \ 21 \ \ \ \ 3\\ \ 1 \ \ \ \ 7 \ \ \ \ 1\\ \ 1 \ \ \ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 2\\ 2\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=2*2*2*2*2*3*7} \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=2^(5) *3*7} \end{gathered}$}`

`\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=672} \end{gathered}$}}}`

Therefore, the least common multiple of 32, 42, and 48 is 672.

`\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}`