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.