Question

What is the LCD of $\dfrac{5}{6}$ and $\dfrac{2}{9}$ ?

Answer 1

Hint: LCD is the smallest number that can be the denominator for a set of fractions. It is also known as the smallest common denominator or we can say that is the smallest number that we can use as a common denominator to create a set of equivalent fractions that all have the same denominator.

Complete step-by-step solution:
LCD stands for least common denominator. So, in order to find the LCD first we need to convert all integers and mixed numbers (mixed fractions) mainly into fractions and then we need to find the least common multiple of all the denominators and the number that we attain is the same as LCD i.e., least common denominator.
Now for the given question, initially we look at the denominators that are 6 and 9 respectively of the two given fractions.
Now we will do the prime factor of both the denominators as $6=3\times 2$ and $9=3\times 3$ .
Now what we will do is we will take all the prime factors to their highest degree present in the prime factors which is $2\times 3\times 3=18$ .
So now we get, $\dfrac{5}{6}=\dfrac{15}{18}$ and similarly we get $\dfrac{2}{9}=\dfrac{4}{18}$ .
Now we can see that the denominators of both the fractions are the same and hence we can do addition, subtraction of these two fractions easily and reduce our calculation time or we can say we can reduce the chances of error to occur.
Hence,for the given fraction the LCD is 18.

Note: While writing the LCD we are aware of the term D that it is a denominator not divisor which is a very common mistake. We must be aware of the similar terms as they sometimes confuse us and lead to huge mistakes.