Question

The LCM of 7 and 13 is

Answer 1

Hint: In this type of question we have to use the concept of factorisation. We know that there are different methods of finding LCM of the given numbers. Here, we use the method of common division. In this method we write the given numbers in one row separated by using commas. Then we divide the numbers by common prime factor. We put the quotient directly under the numbers in the next row. If the number is not divided exactly, then we bring it down in the next row. We will continue this till we get all 1’s in the last row. And finally to obtain LCM, we multiply all prime numbers by which we have divided.

Complete step-by-step solution:
Now, we have to find the LCM of 7 and 13, so we use the method of common division as follows:
\[\begin{align}
  & 7\left| \!{\underline {7,13 \,}} \right. \\
 & 13\left| \!{\underline {1,13 \,}} \right. \\
 & \left| \!{\underline {1,1 \,}} \right. \\
\end{align}\]
Hence, the LCM is given by,
\[\begin{align}
  & \Rightarrow LCM=7\times 13 \\
 & \Rightarrow LCM=91 \\
\end{align}\]
Hence, the LCM of 7 and 13 is 91.

Note: In this type of question students may use another method of finding LCM as there are many more methods. One of the students may use the method of prime factorisation as follows:
First we will find out prime factors of given numbers.
\[\begin{align}
  & \Rightarrow \text{Prime factors of 7 = 1}\times \text{7} \\
 & \Rightarrow \text{Prime factors of 13 = 1}\times 13 \\
\end{align}\]
Now, we know that LCM is a product of common factors with highest power and all other non-common factors. We can see that there is no common factor for 7 and 13 except 1.
Hence, the LCM is given by,
\[\begin{align}
  & \Rightarrow LCM=7\times 13 \\
 & \Rightarrow LCM=91 \\
\end{align}\]
Hence, the LCM of 7 and 13 is 91.