Determine the number greater than 19 and less than 34 that is divisible by 6 and 10.
A: 60
B: 20
C: 30
D: 24
To find the number that is divisible by both 6 and 10, we need to find the least common multiple (LCM) of 6 and 10.
The prime factorization of 6 is $2\times3$, and the prime factorization of 10 is $2\times5$.
To find the LCM, we need to find the greatest power of each prime factor that appears in either factorization.
The prime factorization of the LCM is $2\times3\times5 = 60$.
The only number greater than 19 and less than 34 that is divisible by 6 and 10 is $\boxed{\textbf{(A)}\ 60}$.