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The problem states that Felipe must choose a number between 55 and 101 that is a multiple of 4, 5, and 10. We need to find all such numbers.

### Step 1: Understand the LCM (Least Common Multiple)
To find numbers that are multiples of 4, 5, and 10, we first need to determine the **LCM** of these numbers:
- The LCM of 4, 5, and 10 is the smallest number divisible by all three. 
  - Prime factorization of 4 = \(2^2\)
  - Prime factorization of 5 = \(5^1\)
  - Prime factorization of 10 = \(2^1 \times 5^1\)

The LCM takes the highest power of each prime factor:
\[
\text{LCM}(4, 5, 10) = 2^2 \times 5^1 = 20
\]
Thus, Felipe must choose a number that is a multiple of **20**.

### Step 2: Find Multiples of 20 Between 55 and 101
We now list the multiples of 20 that fall between 55 and 101:
- \( 20 \times 3 = 60 \)
- \( 20 \times 4 = 80 \)
- \( 20 \times 5 = 100 \)

The multiples of 20 in this range are **60, 80, and 100**.

### Final Answer:
The numbers Felipe could choose are **60, 80, 100**.

Would you like a detailed breakdown of how to find LCMs or work with multiples? 

Here are 5 related questions for further practice:
1. What is the least common multiple of 6, 8, and 12?
2. Find all multiples of 15 between 50 and 150.
3. How do you determine the prime factorization of a number?
4. What are the multiples of 25 between 100 and 250?
5. How do you calculate the greatest common divisor (GCD) of 30, 45, and 60?

Tip: Always check for the least common multiple (LCM) when solving problems that ask for numbers divisible by several factors.

Felipe must choose a number between 55 and 101 that is a multiple of 4, 5, and 10. Write all the numbers that he could choose. If there is more than one number, separate them with commas.

Discover how to find numbers between 55 and 101 that are multiples of 4, 5, and 10. This problem teaches about least common multiples (LCM) and basic number theory, ideal for Grades 6-8.

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