Least Common Denominator (LCD)

The lowest Common Denominator or Least Common Denominator is the Least Common Multiple of the denominators of a set of fractions.
 

👁 Image

Common denominator : when the denominators of two or more fractions are the same. 
Least Common denominator is the smallest of all common denominators. 
Why do we need LCD ? 
It simplifies addition, subtraction and comparing fraction.
Common Denominator can be simply evaluated by multiplying the denominators. In this case, 3 * 6 = 18
 

👁 Image

But that may not always be least common denominator, as in this case LCD = 6 and not 18. LCD is actually LCM of denominators.
Examples : 
 

LCD for fractions 5/12 and 7/15 is 60.
We can write both fractions as 25/60 and
28/60 so that they can be added and 
subtracted easily.

LCD for fractions 1/3 and 4/7 is 21.

 

👁 Image

Example Problem : Given two fractions, find their sum using least common dominator.
Examples: 
 

Input : 1/6 + 7/15 
Output : 19/30
 Explanation : LCM of 6 and 15 is 30. 
 So, 5/30 + 14/30 = 19/30 
Input : 1/3 + 1/6
Output : 3/6
 Explanation : LCM of 3 and 6 is 6. 
 So, 2/6 + 1/6 = 3/6

Note* These answers can be further simplified by Anomalous cancellation. 
 

 

Output : 
 

19/30

Time Complexity: O(log(max(deno1,deno2))) 
Auxiliary Space: O(log(max(deno1,deno2)))