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To find the Least Common Multiple (LCM) of the numbers 26, 13, and 63, we need to follow these steps:

1. **Prime Factorization**:
   - \(26 = 2 \times 13\)
   - \(13 = 13\) (since 13 is a prime number)
   - \(63 = 3^2 \times 7\)

2. **Take the highest powers of all prime factors**:
   - For \(2\), the highest power is \(2^1\) from 26.
   - For \(13\), the highest power is \(13^1\) from both 26 and 13.
   - For \(3\), the highest power is \(3^2\) from 63.
   - For \(7\), the highest power is \(7^1\) from 63.

3. **Multiply these highest powers together**:
   \[
   \text{LCM} = 2^1 \times 13^1 \times 3^2 \times 7^1 = 2 \times 13 \times 9 \times 7
   \]

Let's calculate the LCM step by step:

\[
2 \times 13 = 26
\]
\[
26 \times 9 = 234
\]
\[
234 \times 7 = 1638
\]

Thus, the Least Common Multiple (LCM) of 26, 13, and 63 is **1638**.

Let me know if you'd like further explanation or if you have any questions!

Here are some related questions to explore further:
1. How do you find the greatest common divisor (GCD) of two numbers?
2. What is the relationship between LCM and GCD?
3. Can you find the LCM of three numbers using a different method?
4. How do prime factorizations help in finding the LCM?
5. What is the LCM of other sets of numbers, such as 12, 15, and 20?

**Tip**: When finding the LCM of large numbers, always start with their prime factorizations to simplify the process.

Find the least common multiple of the following numbers: 26, 13, 63.

Learn how to find the least common multiple (LCM) of 26, 13, and 63 using prime factorization. Detailed step-by-step explanation included. Suitable for students in Grades 6-8.

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