Question

Find the LCD for the following set of three tions. 13/33, 13/27, and 7/9

A) 297
B) 891
C) 99
D) 33

Answer 1

The LCD for the fractions 13/33, 13/27, and 7/9 is 297, obtained by finding the least common multiple of the denominators. This is done by taking the highest power of each prime factor that appears in any of the denominators.

Step-by-step explanation:

To find the least common denominator (LCD) for the fractions 13/33, 13/27, and 7/9, we need to determine the smallest number that is evenly divisible by each of the denominators: 33, 27, and 9.

1. First, we factor each denominator into its prime factors:
2. 33 = 3 × 11
3. 27 = 3 × 3 × 3
4. 9 = 3 × 3
5. Next, we take the highest power of each prime number that appears in any of the factorizations to be part of our LCD.
6. The highest power of 3 appearing in the denominators is 3³ (from 27).
7. The prime number 11 appears once (from 33).
8. Therefore, the LCD is 3³ × 11 = 27 × 11 = 297.

The correct answer to the problem is option A) 297, which is the LCD for the given set of fractions.