number, including 𝑛 but excluding 1, find a
number p such that 𝐹(12) ∩ 𝐹(18) = 𝐹(𝑝)
A. 18
B. 6
C. 2
D. 3
Bot
answered
\[F(12)=\{2,3,4,6,12\}\]
\[F(18)=\{2,3,6,9,18\}\]
Their intersection is simply the common elements in the two sets, which are $\{2,3,6\}$. Therefore,
\[F(12)\cap F(18)=\{2,3,6\}=F(6)\]
So $\boxed{\textbf{(B)}\ 6}$ is our answer.
Step-by-Step Bot
answered
First, let's find the factors of 12. The factors of 12 are 2, 3, 4, 6, and 12.
Next, let's find the factors of 18. The factors of 18 are 2, 3, 6, and 18.
The common factors of 12 and 18 are 2, 3, and 6.
Therefore, 𝐹(12) ∩ 𝐹(18) = {2, 3, 6}.
Now, let's find the number p such that 𝐹(p) = {2, 3, 6}.
To do this, we need to find the smallest common multiple of 2, 3, and 6.
The smallest common multiple of 2, 3, and 6 is 6.
Therefore, the number p = 6.
Therefore, the answer is B. 6.
