Least common multiple of 5 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 5 and 13. To solve this, we will identify the multiples of each number and find the smallest multiple that they both share.
Answer
The least common multiple of \(5\) and \(13\) is \(65\).
Answer for screen readers
The least common multiple of 5 and 13 is (65).
Steps to Solve
- Identify the multiples of 5
We start by listing the first few multiples of 5.
$$ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, \ldots $$
- Identify the multiples of 13
Next, we list the first few multiples of 13.
$$ 13, 26, 39, 52, 65, 78, 91, 104, 117, \ldots $$
- Find the smallest common multiple
Now, we look for the smallest number that appears in both lists. The multiples of 5 are all numbers in the form of $5n$, and the multiples of 13 are all numbers in the form of $13m$.
- Identify LCM directly using prime factorization (optional)
In this case, since both numbers are prime, we can also find the LCM by multiplying the two numbers directly.
$$ \text{LCM}(5, 13) = 5 \times 13 = 65 $$
- Conclusion
Thus, the least common multiple of 5 and 13 is 65.
The least common multiple of 5 and 13 is (65).
More Information
The least common multiple is the smallest number that is a multiple of both numbers. Since 5 and 13 are prime, their LCM is simply their product. This can also be helpful in real-life situations like scheduling events or finding common denominators in fractions.
Tips
- Confusing least common multiple (LCM) with greatest common divisor (GCD). Remember, LCM is the smallest shared multiple, while GCD is the largest shared factor.
- Forgetting to check if the numbers are prime, which simplifies the calculation of LCM as the product of the two numbers.
