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

Mar 6, 2018

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.

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:

$2 = 2$
$3 = 3$
$8 = 2 \times 2 \times 2$

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:

$L C M = 2 \times 2 \times 2 \times 3 = 8 \times 3 = 24$

$\frac{1}{2} \left(\frac{12}{12}\right) = \frac{12}{24}$

$\frac{1}{3} \left(\frac{8}{8}\right) = \frac{8}{24}$

$\frac{3}{8} \left(\frac{3}{3}\right) = \frac{9}{24}$