What is the LCM of 16 and 8?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 16 and 8. To solve this, we will find the multiples of both numbers and identify the smallest multiple they share.
Answer
The least common multiple of 16 and 8 is 16.
Answer for screen readers
The least common multiple of 16 and 8 is 16.
Steps to Solve
- List the multiples of each number
First, we can list the multiples of 16 and 8 until we find common multiples.
Multiples of 16:
$16, 32, 48, 64, 80, 96, \ldots$
Multiples of 8:
$8, 16, 24, 32, 40, 48, 56, 64, \ldots$
- Identify the common multiples
Now, let's identify the common multiples from both lists we created:
Common multiples of 16 and 8:
$16, 32, 48, 64, \ldots$
- Find the least common multiple
The least common multiple (LCM) is the smallest number that appears in both lists of multiples. From our lists, the smallest number is:
$$ \text{LCM}(16, 8) = 16 $$
The least common multiple of 16 and 8 is 16.
More Information
The least common multiple is useful in various applications, such as solving problems involving fractions and finding common denominators. In this case, since 8 is a factor of 16, the LCM is simply the larger number, 16.
Tips
- One common mistake is to assume the LCM is always the product of the numbers involved. However, this only happens when the numbers are coprime (have no common factors other than 1). In this case, since 8 is a factor of 16, the LCM is the larger number.
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