Question

The LCM of smallest two digit composite number and smallest composite number is
A. $12$
B. $4$
C. $20$
D. $44$

Answer 1

Hint: As we know for any integers, the LCM is the smallest positive integer that is evenly divisible by the integers given. For example, LCM of $\left( {4,5} \right) = 20$ . We find the integers and find their LCM. It is also known that the composite number is the number which has other smaller factors other than $1$ and the number itself. In the given question we will obtain the numerical value of given composite numbers and then LCM can be calculated by finding the factors.

Complete step-by-step answer:
Let us represent the data numerically:
The smallest two digit composite number is $10$ .
The composite number $10$ is the smallest two digit number and also it has $2$ more factors other than $1$ and $10$ which are $2$ and $5$ .
The smallest composite number is $4$ .
The composite number $4$ is the smallest composite number which has $2$ as a factor other than $1$ and $4$ .
Now, the LCM of $4$ and $10$ is calculated by:
The factors of $4 = 2 \times 2$
The factors of $10 = 2 \times 5$
So, LCM=common multiples $ \times $ other remaining factors
LCM $ = 2 \times 2 \times 5 = 20$
Therefore, the LCM of smallest two digit composite number and smallest composite number is $20$ .
Hence, the option C is correct.

Note: The composite number can be observed by taking factors if there are any other factors except $1$ and number itself and remember to choose the smallest number as given in question. The LCM can be calculated by the above method and also it can be calculated by an alternative method which is by taking division side by side as shown below:
LCM of $4$ and $10$ is:
 $2\left| \!{\overline {\,

  4,10 \\
  2,5 \\
  \,}} \right. $
So, LCM $ = 2 \times 2 \times 5 = 20$