Question

What is the least common denominator for 68 and 56 ?
6
8

𝑎
𝑛
𝑑

5
6

?
(1 point)
Responses

24
24

36
36

48
48

14
Answer
answer
Answered by GPT-4o mini
To find the least common denominator (LCD) for 68 and 56, you need to find the least common multiple (LCM) of the two numbers.

1. **Factor each number into its prime factors**:
- \(68 = 2^2 \times 17\)
- \(56 = 2^3 \times 7\)

2. **Take the highest power of each prime factor**:
- For the prime factor \(2\), the highest power between \(2^2\) and \(2^3\) is \(2^3\).
- For the prime factor \(17\), the highest power is \(17^1\).
- For the prime factor \(7\), the highest power is \(7^1\).

3. **Combine the highest powers**:
\[
\text{LCM} = 2^3 \times 7^1 \times 17^1
\]
\[
= 8 \times 7 \times 17
\]
\[
= 56 \times 17
\]
\[
= 952
\]

Therefore, the least common denominator (LCD) for 68 and 56 is 952.

However, the options you provided do not contain 952. Among the options you listed, none of them are correct in the context of being the least common denominator for 68 and 56. The correct answer needs to be 952.
Answered by GPT-4o mini
The least common denominator (LCD) for 68 and 56 is **952**.

However, if you are limited to the options you provided:

- 24
- 36
- 48
- 14

None of these options are correct for the least common denominator of 68 and 56. The correct answer is **952**. If I can assist you with anything else, please let me know!