To find a number greater than 19 and less than 34 that is divisible by both 6 and 10, we first need to determine the least common multiple (LCM) of these two numbers.
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Find the LCM of 6 and 10:
- The prime factorization of 6 is \(2^1 \times 3^1\).
- The prime factorization of 10 is \(2^1 \times 5^1\).
- The LCM will take the highest power of all prime factors involved:
- \(2^1\), \(3^1\), \(5^1\).
- Thus, the LCM is: \[ LCM(6, 10) = 2^1 \times 3^1 \times 5^1 = 30 \]
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Determine if this number is within the given range:
- We need to check if 30 is between 19 and 34:
- Yes, \(19 < 30 < 34\).
Therefore, the number that is greater than 19 and less than 34 that is divisible by both 6 and 10 is 30.
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