Find the Least Common Denominator of the following

Question

Find LCD of numbers listed:

17/5x^4

11/10x^2

Answer 1

The "least common denominator" does NOT mean the most unusual (less common than others), it means the SMALLEST common denominator. And if it is going to be a "common" denominator it has to have EVERY FRACTIONS DENOMINATOR included in the common denominator. But the smallest denominator that still has everyone' denominator.

Here: The 1st fraction has a denominator of 5x⁴ , broken down, any common denominator to serve the first fraction must have a 5 and four multiplied x's.

The 2nd fraction has a denominator of 10x² , broken down, any common denominator to serve the second fraction must have a 5, 2, and two multiplied x's.

COMMON DENOMINATOR: 1st fraction needs 5 x x x x

2nd fraction needs 5 * 2 * x x

Notice the 1st fraction already has a 5, so we do not need to repeat it to satisfy the 2nd denom.

Also the first fraction already has four x's, and the second fraction only needs two x's, so we do not need to put any more x's in the denom.

So our common denom would be 2 * 5 * x * x * x * x = 10x⁴

(This includes everything the 1st fraction needs and everything the 2nd fraction needs without anything "extra" so it is the LEAST common denominator.)