Find the least common denominator for the given set of denominators.
-24, 54, 3
A)54
B)108
C)72
D)216

Question

Quizplus · Accepted Answer

- Listing the multiples of each denominator:
         - 24: 24, 48, 72, 96, 120, 144, 168, 192, 216 ...
         - 54: 54, 108, 162, 216, 270, 324, 378 ...
         - 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 210, 213, 216 ...
- The least common multiple that all three denominators share is the smallest number that is found in all three lists, which is 216. First, we need to find the prime factorization of each denominator:
24 = 2^3 * 3
54 = 2 * 3^3
3 = 3

Then, we take the highest power of each prime factor:
2^3 * 3^3 = 216

Therefore, the least common denominator is 216, which is answer choice D.

Find the Least Common Denominator for the Given Set of Denominators