A farmer from Baguio wants to place carrots in a basket with 75 and 100 pieces. What is the smallest number of carrots can he equally place inside the baskets?

To find the smallest number of carrots that can be equally placed inside baskets containing 75 and 100 pieces, we need to determine the **Least Common Multiple (LCM)** of 75 and 100. The LCM is the smallest number that is a multiple of both 75 and 100.

### Steps to Find the LCM:

1. **Prime Factorization**:
   - 75 = \( 3 \times 5^2 \)
   - 100 = \( 2^2 \times 5^2 \)

2. **Take the highest power of each prime factor**:
   - For 2: the highest power is \( 2^2 \) (from 100)
   - For 3: the highest power is \( 3^1 \) (from 75)
   - For 5: the highest power is \( 5^2 \) (from both)

3. **Multiply these highest powers together**:
   - LCM = \( 2^2 \times 3^1 \times 5^2 = 4 \times 3 \times 25 = 300 \)

### Conclusion:
The smallest number of carrots that can be equally placed inside baskets of 75 and 100 pieces is **300**.

Would you like further details or have any questions? 

Here are 5 related questions:

1. How do you find the Greatest Common Divisor (GCD) of two numbers?
2. Can the LCM of two numbers ever be smaller than either of the numbers?
3. What is the relationship between GCD and LCM?
4. How would the solution change if the basket sizes were 75 and 120?
5. How do you calculate the LCM of more than two numbers?

**Tip**: Understanding prime factorization is crucial for solving LCM and GCD problems efficiently.

Discover how to determine the smallest number of carrots that can be equally placed inside baskets containing 75 and 100 pieces. Learn about number theory concepts, prime factorization, and the least common multiple (LCM) method used to solve the problem. Suitable for Grades 7-9.

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