https://file.aiquickdraw.com/mathbot/file/17283312902216oju5zs1.jpg

The problem in the image asks to find numbers between 67 and 113 that are multiples of 3, 9, and 12.

To solve this, we need to find the **least common multiple (LCM)** of 3, 9, and 12. This will allow us to identify which numbers in the range [67, 113] are divisible by this LCM.

### Step 1: Find the LCM of 3, 9, and 12
- Factors of 3: \( 3^1 \)
- Factors of 9: \( 3^2 \)
- Factors of 12: \( 2^2 \times 3^1 \)

The LCM is found by taking the highest power of each prime factor:
- For 3: \( 3^2 = 9 \)
- For 2: \( 2^2 = 4 \)

Thus, the LCM is \( 4 \times 9 = 36 \).

### Step 2: Identify multiples of 36 in the range 67 to 113
We now find the multiples of 36 within the interval:
- \( 36 \times 2 = 72 \)
- \( 36 \times 3 = 108 \)

So, the numbers between 67 and 113 that are divisible by 36 are **72** and **108**.

### Final Answer:
The numbers Jenny could choose are **72, 108**.

Would you like any further explanation or details? Here are some related questions:

1. How do you find the LCM of multiple numbers?
2. What are other ways to solve LCM-related problems?
3. How does finding the greatest common divisor (GCD) differ from LCM?
4. Can this approach be applied to other number ranges and multiples?
5. What are some real-world applications of LCM?

**Tip:** Remember, the LCM helps you find common multiples, especially in word problems involving multiple constraints!

Jenny must choose a number between 67 and 113 that is a multiple of 3, 9, and 12. Write all the numbers that she could choose. If there is more than one number, separate them with commas.

Learn how to find multiples of 3, 9, and 12 between 67 and 113 by calculating the least common multiple (LCM). This step-by-step solution identifies numbers that Jenny could choose, covering key concepts like LCM and number theory, suitable for Grades 5-7.

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