Bot GPT 4-o mini To find a number greater than 19 and less than 34 that is divisible by both 6 and 10, we will first find the least common multiple (LCM) of 6 and 10.
The prime factorization of the numbers is:
- \(6 = 2 \times 3\)
- \(10 = 2 \times 5\)
The LCM is found by taking the highest power of each prime factor:
- \(2^1\)
- \(3^1\)
- \(5^1\)
Thus, the LCM is: \[ LCM = 2^1 \times 3^1 \times 5^1 = 30 \]
Next, we will check if 30 is in the range between 19 and 34.
Since \(19 < 30 < 34\), this number satisfies the conditions of being greater than 19 and less than 34.
Finally, we check if it is indeed divisible by both 6 and 10:
- \(30 \div 6 = 5\) (which is an integer)
- \(30 \div 10 = 3\) (which is also an integer)
Therefore, the number greater than 19 and less than 34 that is divisible by both 6 and 10 is: \[ \boxed{30} \]
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