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What is the common factors, gcf, lcm of 10,15,45

To find the common factors, greatest common factor (GCF), and least common multiple (LCM) of the numbers 10, 15, and 45, let's break it down step by step:

### 1. **Common Factors:**
   - **Factors of 10:** 1, 2, 5, 10
   - **Factors of 15:** 1, 3, 5, 15
   - **Factors of 45:** 1, 3, 5, 9, 15, 45
   
   The common factors of 10, 15, and 45 are **1** and **5**.

### 2. **Greatest Common Factor (GCF):**
   The greatest common factor is the largest number that is a factor of all three numbers.
   
   - The GCF of 10, 15, and 45 is **5**.

### 3. **Least Common Multiple (LCM):**
   The LCM is the smallest number that is a multiple of all three numbers.

   - **Prime factorization:**
     - 10 = \(2 \times 5\)
     - 15 = \(3 \times 5\)
     - 45 = \(3^2 \times 5\)
     
   - The LCM is found by taking the highest power of each prime factor:
     - \(2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90\)
     
   - The LCM of 10, 15, and 45 is **90**.

### Summary:
- **Common Factors:** 1, 5
- **GCF:** 5
- **LCM:** 90

Would you like more details or have any questions?

### Related Questions:
1. How do you find the GCF of two numbers using the Euclidean algorithm?
2. Can you explain how to find the LCM of two numbers using their prime factorizations?
3. What is the relationship between the GCF and LCM of two numbers?
4. How would the GCF and LCM change if one of the numbers was a prime number?
5. How do the GCF and LCM concepts extend to more than three numbers?

### Tip:
When calculating the LCM of multiple numbers, using prime factorization ensures you include all necessary factors, leading to the correct minimum common multiple.

Learn how to find the common factors, greatest common factor (GCF), and least common multiple (LCM) of the numbers 10, 15, and 45 with step-by-step explanations. Understand the concepts of factors, GCF, LCM, and prime factorization. Suitable for students in Grades 6-8.

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