Question

What is the LCD of 5/12 and -9/16 ?

Answer 1

You are looking for the least common multiple (LCM) of 12 and 16.

To find the LCD or LCM, first find the prime factorizations of the numbers.

\(12 = 2^2 \times 3\)

\(16 = 2^4\)

The LCM or LCD is the product of all factors that are not common, and common with the higher exponent.

Both numbers have factor 2. Since the use 2^2 and 2^4, use the higher exponent, 2^4.
Then 12 also has the factor 3. it is a non-common factor, so use it too.

The LCM is \(2^4 \times 3 = 8 \times 3 = 24\)