College

The students in a class can be divided into groups of 3, 4, 6, and 9. What is the least number of students this class can have?

A. 18
B. 28
C. 36
D. 72

Answer :

To find the least number of students in the class that can be divided into groups of 3, 4, 6, and 9, we need to determine the smallest number that is a multiple of each of these group sizes. This is known as the least common multiple (LCM).

Here's how you can find the LCM for the numbers 3, 4, 6, and 9:

1. List Prime Factors:

- 3 is already a prime number.
- 4 can be factored into 2 × 2.
- 6 can be factored into 2 × 3.
- 9 can be factored into 3 × 3.

2. Select the Highest Power of Each Prime Number Present:

- For the number 2, the highest power present in our numbers is [tex]\(2^2\)[/tex] (from the number 4).
- For the number 3, the highest power present is [tex]\(3^2\)[/tex] (from the number 9).

3. Multiply the Highest Powers of All Prime Factors:

So, the LCM is calculated as:
[tex]\[
2^2 \times 3^2 = 4 \times 9 = 36
\][/tex]

Thus, the smallest number of students that can form groups of 3, 4, 6, and 9 is 36. The correct option is:

c. 36