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

A math teacher divides the class into groups to solve exercises together.

On Tuesday, he divides them into groups of 6.

On Wednesday, he divides them into groups of 4.

The division is exact and no student is left without a group.

The number of students in a class is more than 21 but less than 31.

How many students are in the class?

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 $24$.