Question

What is the lowest common denominator of $\dfrac{3}{4}$ and $\dfrac{5}{8}$?

Answer 1

Hint: For solving this question you should know about the least common denominator or lowest common denominator of a fraction. The least common denominator is the value of denominator which can be divided by all the denominators of the fractions and this denominator is also known as lowest common denominator because we take the smallest value in it as a denominator. In this question we have to find the least common denominator of $\dfrac{3}{4}$ and $\dfrac{5}{8}$. So, we will do the basic calculations and find our answer.

Complete step-by-step solution:
According to our question we have to calculate the lowest common denominator of $\dfrac{3}{4}$ and $\dfrac{5}{8}$.
Let us consider $\dfrac{3}{4}$. If we multiply the numerator and denominator by the same number then the fraction remains the same. Similarly, if we multiply numerator and denominator in the other fraction then too it will be the same number as before. If we notice then it is clear that we can add, subtract or compare these three fractions, only if their denominators are the same. Hence only the purpose of finding the least common denominator or lowest common denominator is to identify a common denominator, to which all the denominators can be raised.
If we increase 4 to : 8, 12, 16, 20, 24, 28, 32, 36, 40… and so on by multiplying it by 2, 3, 4, 5, 6… and so on.
Similarly, if we increase 8 to 16, 24, 32, 40, 48, 56…and so on by multiplying it by 2, 3, 4, 5, 6… and so on.
In all these the common denominators are 8, 16, 32, 40… and more. But we have to calculate the lowest common denominator. Then it will be 8.
We can check this by performing any arithmetic task . If we add them, then,
$\begin{align}
  & \Rightarrow \dfrac{3}{4}+\dfrac{5}{8}=\dfrac{3}{4}\times \dfrac{2}{2}+\dfrac{5}{8} \\
 & \Rightarrow \dfrac{6}{8}+\dfrac{5}{8}=\dfrac{11}{8} \\
\end{align}$
So, it is done and the addition is $\dfrac{11}{8}$.
So, the lowest common denominator is 8.

Note: During calculating the least common denominator and lowest common denominator it is important to make the denominator as a number which is divided by all denominators of the fraction. And it will be the lowest number for that operation which will be divided by all denominators. Also, we need to be attentive while reading the question and then solving it.