Question

What is the least common multiple of 18 and 24?

Answer 1

Hint: We know that the least common multiple is also known as LCM. We will use a prime factorisation method to find the LCM of the given two numbers. We will write each of the given numbers as the product of its prime factors and the LCM contains the factor of each number, but without any duplicates.

Complete step-by-step solution
We have been asked to find the LCM or least common multiple of 18 and 24.
We will use the prime factorisation method to find the LCM of 18 and 24. Firstly, we will write 18 and 24 as the products of its prime factors and the LCM contain the factor of each number, but without any duplicates.
Prime factorisation of 18 is as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  18 \,}} \right. \\
 & \ 3\left| \!{\underline {\,
  9 \,}} \right. \\
 & \ 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & \ \ \ \left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
So, we can write $18=2\times 3\times 3$.
Again, Prime factorisation of 24 is as follows:
\[\begin{align}
  & 2\left| \!{\underline {\,
  24 \,}} \right. \\
 & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & \ 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & \ 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & \ \ \ \left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
So, we can write $24=2\times 2\times 2\times 3$.
We have,
$18=2\times 3\times 3$
$24=2\times 2\times 2\times 3$
We know that the LCM contains the factor of each number, but without any duplicates.
$\begin{align}
  & \Rightarrow LCM\ of\ 18\ and\ 24=2\times 3\times 2\times 3\times 2 \\
 & =72 \\
\end{align}$
Therefore, the LCM or least common multiple of 18 and 24 is 72.

Note: Remember the properties of LCM that the LCM of two or more numbers cannot be less than any of them. Also, if a number is the factor of another number, their LCM is the greater number itself.We can also solve it by another method in which first we will write the multiples of 18 and 24 separately and then find common multiples between them and the least value will be equal to LCM or least common multiple.