Divisibility Problem: Finding Number of Students Divisible by Both 6 and 4

To solve this problem, we'll follow these steps:

• Calculate the LCM of 6 and 4.
• Find the number between 21 and 31 that is a multiple of this LCM.

Step 1: Calculate the LCM of 6 and 4.
- The prime factorization of 6 is $2 \times 3$.
- The prime factorization of 4 is $2^2$.
- The LCM is derived by taking the highest power of each prime number involved: $LCM(6, 4) = 2^2 \times 3 = 12$.

Step 2: Identify the multiples of 12 within the range (21, 31).
- Multiples of 12 are: $12, 24, 36, \ldots$
- In the range between 21 and 31, the only multiple of 12 is 24.

Therefore, the number of students in the class is $24$.