On Monday, the students in Mr. Carson’s class worked in pairs. On Tuesday, the students worked in groups of 3. On Wednesday, the students worked in groups of 4. Each day the students made equal groups with no student left out of a group. How many students could be in Mr. Carson’s class?

The smallest number of students in the class is the smallest number that is divisible by 2, 3, and 4. You need the least common multiple of 2, 3, and 4.
This is like finding the least common denominator.

Find the prime factors of the three numbers:
2 = 2
3 = 3
4 = 2^2

To find the LCM you need common factors, and not common factors with the larger exponent.

Now single factor is common to all numbers.
There is 2 and 2^2, so use 2^2 since it has the larger exponent.
There is also a 3, so use the 3.

LCM = 2^2 * 3 = 4 * 3 = 12

Mr. Carson's class may have 12 students. 12 is the smallest number of students it can have.