lcm of 8 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 8 and 13. To find the LCM, we typically identify the multiples of each number and determine the smallest multiple that they both share.
Answer
The least common multiple of 8 and 13 is 104.
Answer for screen readers
The least common multiple of 8 and 13 is 104.
Steps to Solve
- List the multiples of each number
Start by listing a few multiples of 8 and 13:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ...
- Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ...
- Identify the common multiples
Now look for the common multiples in the two lists. A common multiple is a number that appears in both lists.
- Common multiples from the lists:
- For our given numbers, 8 and 13, we can see there are no common values in the two lists for the multiples we've written.
- Calculate the least common multiple using the formula
Since 8 and 13 are relatively prime (they have no common factors other than 1), you can find the LCM by multiplying the two numbers:
$$ \text{LCM}(8, 13) = \frac{8 \times 13}{\text{GCD}(8, 13)} $$
Since the GCD of 8 and 13 is 1, we have:
$$ \text{LCM}(8, 13) = \frac{8 \times 13}{1} = 104 $$
- Conclusion
Thus, the least common multiple of 8 and 13 is 104.
The least common multiple of 8 and 13 is 104.
More Information
The least common multiple (LCM) is an important concept in mathematics, often used to find common denominators for fractions. In this case, since 8 and 13 share no factors besides 1, their LCM is simply their product, 104.
Tips
- Forgetting to check if the numbers have common factors. When numbers are relatively prime, it’s easier to compute the LCM by multiplying them directly.
- Not understanding the definition of LCM can lead to incorrect assumptions about how to find it.
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