LCM of 26 and 39
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 26 and 39. To find the LCM, we can use the prime factorization of each number or find the multiples of each number until we identify the smallest common multiple.
Answer
The least common multiple (LCM) of 26 and 39 is $78$.
Answer for screen readers
The least common multiple (LCM) of 26 and 39 is $78$.
Steps to Solve
- Find the prime factorization of each number
To find the least common multiple (LCM), we start by finding the prime factorization of 26 and 39.
- The prime factorization of 26 is $2 \times 13$.
- The prime factorization of 39 is $3 \times 13$.
- Identify the unique prime factors
Next, we identify all the unique prime factors from both factorizations.
- The unique prime factors are $2$, $3$, and $13$.
- Use the highest power of each prime factor
Now, we will take the highest power of each unique prime factor to find the LCM.
- For $2$, the highest power is $2^1$.
- For $3$, the highest power is $3^1$.
- For $13$, the highest power is $13^1$.
- Multiply the highest powers together
Finally, we multiply these highest powers together to find the LCM:
$$ LCM = 2^1 \times 3^1 \times 13^1 = 2 \times 3 \times 13 $$
Calculating gives us:
$$ 2 \times 3 = 6 $$
Then, we multiply:
$$ 6 \times 13 = 78 $$
Thus, the LCM of 26 and 39 is 78.
The least common multiple (LCM) of 26 and 39 is $78$.
More Information
The LCM is important in various mathematical applications, especially in adding and subtracting fractions. The least common multiple ensures that fractions can be combined effectively.
Tips
- Forgetting to include all unique prime factors: Ensure to consider all prime factors from both numbers to avoid missing any contributions to the LCM.
- Incorrectly multiplying the prime factors: Double-check the multiplication to ensure accuracy when calculating the LCM.
