Question

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

Answer 1

Hint: In order to solve this question, we should know about the concept of LCM or least common multiple. Least common multiple is nothing but the smallest number which is the multiple of the numbers whose LCM is being taken. So, to solve this, we will find the LCM by division method.

Complete step-by-step answer:
To solve this question, we should know what LCM means. LCM is the smallest number which is a multiple of the numbers of which we are taking the LCM. So, we will use the division method to get the answer, by finding the common prime numbers to divide 4, 5 and 8 until we get 1, 1 and 1 as the least numbers. And then we will multiply all the factors. So, we can write the division as follows.
$\begin{align}
  & 2\left| \!{\underline {\,
  4,5,8 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2,5,4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,5,2 \,}} \right. \\
 & 5\left| \!{\underline {\,
  1,5,1 \,}} \right. \\
 & \text{ }1,1,1 \\
\end{align}$
So, we can say that the LCM of the numbers 4, 5 and 8 is $2\times 2\times 2\times 5=40$.

Note: We can also find the LCM of the numbers 4, 5 and 8 by writing their factors individually and then multiplying all those factors with their highest power of occurrence. Let us consider the factors of each number as below,
$\begin{align}
  & 4=2\times 2 \\
 & 5=5\times 1 \\
 & 8=2\times 2\times 2 \\
\end{align}$
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.