Determine the greater number than 19 and less than 34 that is divisible by 6 and 10.
To solve this problem, we need to find the least common multiple (LCM) of 6 and 10.
The prime factors of 6 are 2 and 3.
The prime factors of 10 are 2 and 5.
To find the LCM, we multiply the highest power of each prime factor:
2^1 * 3^1 * 5^1 = 30
Therefore, the LCM of 6 and 10 is 30.
Now, we need to find the multiples of 30 that are greater than 19 and less than 34. We can start by determining the multiples of 30 less than 34:
30 * 1 = 30 (not within the range)
30 * 2 = 60 (not within the range)
30 * 3 = 90 (not within the range)
...
We can see that the first multiple of 30 within the range is 30 * 1 = 30.
Therefore, the answer is 30.