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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
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
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