To determine which number is a multiple of both 6 and 8, we need to follow these steps:
1. Understand Multiples and LCM:
- A number that is a multiple of both 6 and 8 must be a multiple of their Least Common Multiple (LCM).
2. Find the LCM of 6 and 8:
- LCM stands for Least Common Multiple. It is the smallest number that is a multiple of both 6 and 8.
- To find the LCM, we can use the Greatest Common Divisor (GCD). The LCM of two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] can be found using the formula:
[tex]\[
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
\][/tex]
- For 6 and 8:
- The GCD of 6 and 8 is 2.
- Hence, the LCM is [tex]\(\frac{6 \times 8}{2} = 24\)[/tex].
3. Check the Choices:
- We need to verify which of the given choices are multiples of 24.
- The choices are:
- 2
- 0
- 3
- 24
- 18
4. Verify Each Choice:
- 2: Not a multiple of 24.
- 0: 0 is technically a multiple of any number, including 24.
- 3: Not a multiple of 24.
- 24: 24 is exactly the LCM of 6 and 8, hence a multiple of 24.
- 18: Not a multiple of 24.
Given this analysis, the number in the choices that is a multiple of both 6 and 8 is:
- 0
