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# Least Common Denominator

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The Fractions are numbers which can be expressed in form of $\frac{p}{q}$, where ‘p’ and ‘q’ are whole Numbers and q ≠ 0. There are two types of fractions: like and unlike fractions. Like fractions are the fractions with same denominator, and unlike fractions are the fractions with different denominators.We can convert an unlike fraction to a like fraction by finding the LCM of the denominators of all fractions and converting all the denominators to a common denominator value. This common denominator is called the least common denominator or the lowest common denominator.

Thus we can define the least common denominator as the LCM of the denominators of all the unlike fractions given in a question. We know that fractions can be compared only if they are like. Also to add or subtract the fractions, the fractions must be like fractions. But that doesn’t mean that we can’t compare or add or subtract unlike fractions. To do such mathematical operations with unlike fractions, we need to first change them to like fractions & thus need to find the least common denominator. This can be explained by an example:

Example:
Add $\frac{3}{7}$ & $\frac{4}{5}$
Multiples of 7 are 7, 14, 21, 28, 35,.....
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35,.......
The LCM of 7 & 5 is 35
The LCD of the two fraction is 35.
$\frac{3}{7}$ + $\frac{4}{5}$
= $\frac{3*5}{7*5}$ + $\frac{4*7}{5*7}$
= $\frac{15}{35}$ + $\frac{28}{35}$
= $\frac{43}{35}$