Question

Find the LCM of the numbers 4, 5 and 8.

\begin{align} & 2\left| \!{\underline {\, 4,5,8 \,}} \right. \\ & 2\left| \!{\underline {\, 2,5,4 \,}} \right. \\ & 2\left| \!{\underline {\, 1,5,2 \,}} \right. \\ & 5\left| \!{\underline {\, 1,5,1 \,}} \right. \\ & \text{ }1,1,1 \\ \end{align}
So, we can say that the LCM of the numbers 4, 5 and 8 is $2\times 2\times 2\times 5=40$.
\begin{align} & 4=2\times 2 \\ & 5=5\times 1 \\ & 8=2\times 2\times 2 \\ \end{align}
Now the factors are 2 and 5. The powers of these in each number are ${{2}^{2}},{{5}^{1}},{{2}^{3}}$ . The highest power of factor 2 is 3 and the highest power of factor 5 is 1, so we get the LCM as ${{2}^{3}}\times 5$, which is 40.