Question

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

Answer 1

12

Explanation:

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.

Answer 2

24

Explanation:

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`