The lowest Common Denominator or Least Common Denominator is the Least Common Multiple of the denominators of a set of fractions.
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
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
LCD for fractions 1/3 and 4/7 is 21.
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.
Time Complexity: O(log(max(deno1,deno2))) Auxiliary Space: O(log(max(deno1,deno2)))
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