Find the LCM and GCF of each set of numbers             1.)7 and 21

To find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of the numbers 7 and 21, we can follow these steps:

### Step 1: Find the GCF
The Greatest Common Factor (GCF) is the largest factor that divides both numbers.

- **Factors of 7:** 1, 7
- **Factors of 21:** 1, 3, 7, 21

The common factors of 7 and 21 are 1 and 7. The greatest of these is **7**.

So, **GCF(7, 21) = 7**.

### Step 2: Find the LCM
The Least Common Multiple (LCM) is the smallest multiple that is divisible by both numbers.

- **Multiples of 7:** 7, 14, 21, 28, 35, ...
- **Multiples of 21:** 21, 42, 63, 84, ...

The smallest common multiple is **21**.

So, **LCM(7, 21) = 21**.

### Summary
- **GCF(7, 21) = 7**
- **LCM(7, 21) = 21**

Would you like more details on the process or have any questions?

Here are some related questions:

1. What are the GCF and LCM of 8 and 12?
2. How do you find the GCF and LCM of 15 and 25?
3. What is the GCF and LCM of 9 and 27?
4. How do prime factorization help in finding the GCF and LCM?
5. Can the GCF ever be greater than the LCM?

**Tip:** The GCF is useful for simplifying fractions, while the LCM is important for finding a common denominator.

Learn how to find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of numbers 7 and 21 with a step-by-step explanation. Understand the concept of LCM and GCF in number theory. Suitable for students in Grades 5-6.

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