Question

How do you find the LCD of $\dfrac{11}{6}$ and $\dfrac{3}{10}$ ?

Answer 1

Hint: At first we make the multiplication tables of the numbers of which we need to find out the LCD. We sort out the common multiples of the numbers and find the least among the common multiples.

Complete step by step answer:
The two fractions given are
$\dfrac{11}{6}$ and $\dfrac{3}{10}$
The denominator of the first fraction is $6$ and that of the second fraction is $10$ .
LCD means Lowest Common Denominator. This means that we need to find a common denominator of the two fractions, such that the fractions remain same and at the same time, the common denominator is also the lowest possible natural number. These two conditions, if satisfied, can declare the common denominator to be the lowest common denominator.
Now, let us have a look at the multiplication tables of $6$ and $10$ .
\[\begin{align}
  & 6\times 1=6 \\
 & 6\times 2=12 \\
 & 6\times 3=18 \\
 & 6\times 4=24 \\
 & 6\times 5=30\triangleleft \\
 & 6\times 6=36 \\
 & 6\times 7=42 \\
 & 6\times 8=48 \\
 & 6\times 9=54 \\
 & 6\times 10=60\triangleleft \\
\end{align}\] $\begin{align}
  & 10\times 1=10 \\
 & 10\times 2=20 \\
 & 10\times 3=30\triangleleft \\
 & 10\times 4=40 \\
 & 10\times 5=50 \\
 & 10\times 6=60\triangleleft \\
 & 10\times 7=70 \\
 & 10\times 8=80 \\
 & 10\times 9=90\triangleleft \\
 & 10\times 10=100 \\
\end{align}$
Upon comparison, we can see that the common multiples of $6$ and $10$ are $30,60,90$ and so on. These multiples are shown as the numbers marked separately on the respective multiplication tables. Out of these common multiples, we see that $30$ is the smallest or the lowest common multiple.
Now, we need to convert the given fractions to their equivalent fractions having \[30\] as the denominator. We start with the first fraction $\dfrac{11}{6}$ . $6\times 5=30$ and we know that if we multiply the numerator and denominator of a fraction by the same number, then we get an equivalent fraction. So, we multiply the numerator and denominator of $\dfrac{11}{6}$ with $5$ .
$\Rightarrow \dfrac{11\times 5}{6\times 5}=\dfrac{55}{30}$
We do the same thing with $\dfrac{3}{10}$ . As, $10\times 3=30$ , we multiply the numerator and denominator of $\dfrac{3}{10}$ with $3$ . We get,
$\Rightarrow \dfrac{3\times 3}{10\times 3}=\dfrac{9}{30}$
Having satisfied all the two required conditions, we can now conclude that $30$ is the LCD of $\dfrac{11}{6}$ and $\dfrac{3}{10}$ .

Note:
We must be very careful when finding out the LCD of two fractions or the LCM of two numbers. Sometimes, students consider a common multiple as the LCD which is not the lowest. This, though doesn’t lead to wrong answers, it only requires simplification in the end which is irrelevant.