Find the product of the least common multiple (LCM) of $8$ and $6$ and the greatest common divisor (GCD) of $8$ and $6$.
To find the LCM of $8$ and $6$, I need to find the smallest positive integer that is a multiple of both $8$ and $6$. One way to do this is to list the multiples of $8$ and $6$ and look for the first common one. The multiples of $8$ are $8, 16, 24, 32, 40, \dots$. The multiples of $6$ are $6, 12, 18, 24, 30, 36, \dots$. I can see that $24$ is the first common multiple of $8$ and $6$, so the LCM of $8$ and $6$ is $24$. To find the GCD of $8$ and $6$, I need to find the largest positive integer that is a factor of both $8$ and $6$. One way to do this is to list the factors of $8$ and $6$ and look for the largest common one. The factors of $8$ are $1, 2, 4, 8$. The factors of $6$ are $1, 2, 3, 6$. I can see that $2$ is the largest common factor of $8$ and $6$, so the GCD of $8$ and $6$ is $2$. Now I have the LCM and the GCD of $8$ and $6$, and I need to find their product. The product of $24$ and $2$ is $48$. 