Determine the number greater than 19 and less than 34 that is divisible by 6 and 10.(1 point)

Question

Responses

30
30

20
20

60
60

24

Answer 1

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.