To solve the problem, we need to find a number between 19 and 34 that is divisible by both 6 and 10.
First, let's determine the least common multiple (LCM) of 6 and 10.
- The prime factorization of 6 is \(2 \times 3\).
- The prime factorization of 10 is \(2 \times 5\).
The LCM is found by taking the highest power of each prime number that appears in the factorization:
- The LCM of 6 and 10 is \(2^1 \times 3^1 \times 5^1 = 30\).
Now, we check if 30 is between 19 and 34:
- 19 < 30 < 34
Thus, 30 is a valid solution.
Next, let's check the options provided:
- 30 ✅
- 20 ❌ (not divisible by both)
- 60 ❌ (greater than 34)
- 24 ❌ (not divisible by 10)
Therefore, the number that is greater than 19 and less than 34 that is divisible by both 6 and 10 is 30.
1 answer