Question

What is the least common multiple of 2, 3 and 7?

Answer 1

Hint: In the given question, we have to find the least common multiple of three numbers. So, we use the least common multiple to solve and get the solution. As we know that the least common multiple is between two or more than two integers, such that it is the smallest positive number which is divisible by all the integers. So, we first find the factors of all 2, 3 and 7 individually using the prime factorisation method. After getting the factors, we will find the least factor between them to get the required solution.

Complete step by step answer:
According to the given question, we have to find the least common multiple of three numbers. So, we will use the least common multiple (LCM) method to get the solution.
The given numbers are 2, 3 and 7 ………(1)
So, now, we will first find the least common multiple of 2 to get the factors for the same. So, 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,
$2\times 1\ldots \ldots \ldots \left( 2 \right)$
Now, to get the factors, we will find the least common multiple of 3.
$\begin{align}
  & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Thus, the least common multiple of 3 is equal to,
$3\times 1\ldots \ldots \ldots \left( 3 \right)$
Now, to get the factors, we will find the least common multiple of 7.
$\begin{align}
  & 7\left| \!{\underline {\,
  7 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$

Thus, the least common multiple of 7 is equal to,
$7\times 1\ldots \ldots \ldots \left( 4 \right)$
So, for the least common multiple, we have to find the highest factor of 2, 3 and 7. Thus from the values of equation (2), (3) and (4), we get the LCM as the product of 2, 3 and 7, so we get,
$2\times 3\times 7=42$

Therefore, the least common multiple of 2, 3 and 7 is 42.

Note: We have to solve the question step by step properly to avoid confusion and errors. You can also find the LCM of two numbers together by this formula, $LCM\left( a,b \right)=\dfrac{a\times b}{GCD\left( a,b \right)}$, where we substitute the value of the first number as ‘a’ and ‘b’ as the second number.