Question

What is the least common multiple of $2$ and $12$ ?

Answer 1

Hint: In this question, we have to find the least common multiple of two numbers. Thus, we will use the least common multiple method to get the solution. As we know, the least common multiple is between two or more than two integers, such that it is the smallest positive integer that can be divisible by all the integers. So, we start solving this problem, by finding the factors of both 2 and 12 individually using the least common multiple method. After that, we will see the least factors between them, to get the required solution.

Complete step by step solution:
According to the problem, we have to find the least common multiple of two numbers.
Thus, we will use the LCM method to get an accurate solution
The numbers given to us is $2$ and $12$ ---------- (1)
So, now we will first find the least common multiple of $2$ to get the factors for the same, we get
$\begin{align}
  & 2\left| \!{\underline {\,
 2 \,}} \right. \\
 & 1\left| \!{\underline {\,
 1 \,}} \right. \\
\end{align}$
Thus, the least common multiple of $2$ is equal to $2\times 1$ --------- (2)
Now, to get the factors we will find the least common multiple of $12$, we get
\[\begin{align}
  & 2\left| \!{\underline {\,
 12 \,}} \right. \\
 & 2\left| \!{\underline {\,
 6 \,}} \right. \\
 & 3\left| \!{\underline {\,
 3 \,}} \right. \\
 & 1\left| \!{\underline {\,
 1 \,}} \right. \\
\end{align}\]
Therefore, the LCM of $12$ is equal to $2\times 2\times 3\times 1={{2}^{2}}\times 3=4\times 3$ ------------ (3)
So, for the least common multiple, we have to find the highest factor of $2$ and $12$ , thus from value of equation (2) and (3), we get the LCM as the product of 4 and 3, we get
$LCM\left( 2,12 \right)=4\times 3=12$
Therefore, the least common multiple of $2$ and $12$ is equal to $12$.

Note: While solving this problem, do the step by step calculations properly to avoid confusion and errors. You can also find the LCM of both the numbers together. One of the alternative methods to solve this problem is using the formula $LCM\left( a,b \right)=\dfrac{a\times b}{GCD\left( a,b \right)}$ , where substitute the value a as equal to 2 and b as equal to 12, to get an accurate solution.