The LCD for the fractions 1/3, 3/4, 5/32, and 8/9 is
A. 24.
B. 64.
C. 288.
D. 3072.
can u show me how to do this
288
Try the other numbers by dividing by each of the denominators.
To find the Least Common Denominator (LCD) for a set of fractions, you need to find the least common multiple (LCM) of their denominators.
Step 1: Find the individual denominators of the fractions - 3, 4, 32, and 9.
Step 2: Determine the prime factorization of each denominator:
- 3 = 3
- 4 = 2^2
- 32 = 2^5
- 9 = 3^2
Step 3: Identify the highest powers of all the prime factors that appear in any of the denominators:
- 2^5 = 32
- 3^2 = 9
Step 4: Multiply the highest powers together:
- 32 * 9 = 288
The LCD for the fractions 1/3, 3/4, 5/32, and 8/9 is 288.
Therefore, the correct answer is C. 288.
Find the smallest number that all of the denominators go into evenly.
Well -- 24 is out because it's smaller than 32.
64 is out because it isn't evenly divisible by 9.