What is the least common denominator of 1/2, 2/3, and 3/8?

Question

Genesis Amaya · Accepted Answer

12

8 is a multiple of 2. 8/2 is 4. 3 is not a multiple of either 8 nor 2. 4*3 is 12. I know that this is really not an adequate answer and I can't remember how we used to do it in pre-algebra but I know 12 is the right answer.

Emery Allen · Answer

24

When calculating a common denominator, we are, in essence, finding the Least Common Multiple of the denominators of the fractions. So let's do that by using prime factorizations: #2=2# #3=3# #8=2xx2xx2# We clearly need 2s and 3s, but how many? For the 2s, the largest grouping is in the 8. There are 3 2s and so we need 3 2s. We also need a 3 because of the 3. And so we have: #LCM=2xx2xx2xx3=8xx3=24# #1/2(12/12)=12/24# #1/3(8/8)=8/24# #3/8(3/3)=9/24#

Gianna Caruso · Answer

undefined To find the least common denominator (LCD) of $ \frac{1}{2} $, $ \frac{2}{3} $, and $ \frac{3}{8} $, we need to find the smallest common multiple of the denominators, which are 2, 3, and 8.

The prime factorization of 2 is $2^1$, the prime factorization of 3 is $3^1$, and the prime factorization of 8 is $2^3$.

To find the LCD, we take the highest power of each prime factor that appears in the factorizations:

$$ 2^3 \times 3^1 = 8 \times 3 = 24 $$

So, the least common denominator (LCD) is 24.