Find the least common denominator for the given set of denominators.
-56, 48
A)672
B)168
C)336
D)112

Question

Quizplus · Accepted Answer

To find the least common denominator, we need to find the smallest multiple that both 56 and 48 share.

Prime factorizing both numbers: 
56 = 2^3 * 7 
48 = 2^4 * 3

To find the least common multiple, we take the highest power of each prime factor: 
LCM = 2^4 * 3 * 7 = 336

Therefore, the least common denominator is 336, which is choice C. To find the least common denominator (LCD) of 56 and 48, we need to find their prime factorizations:

56 = 2^3 * 7 
48 = 2^4 * 3

Then, the LCD should include all the factors of both numbers, but we only need to include each factor once. Therefore, we take the highest power of each prime factor that appears in either prime factorization:

LCD = 2^4 * 3 * 7 = 336

Therefore, the best choice is C.

Find the Least Common Denominator for the Given Set of Denominators