What is the least common multiple of 9 and 27?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 27. To find the LCM, we need to identify the smallest number that is a multiple of both 9 and 27.
Answer
The least common multiple of 9 and 27 is \( 27 \).
Answer for screen readers
The least common multiple of 9 and 27 is ( \text{LCM}(9, 27) = 27 ).
Steps to Solve
- Identify the multiples of each number
First, let's list some multiples of 9:
- 9, 18, 27, 36, 45, 54, ...
Now, let's list some multiples of 27:
- 27, 54, 81, 108, ...
- Find the common multiples
Next, we need to look for common multiples from the lists above. By comparing:
- From the multiples of 9, we have: 9, 18, 27, 36, 45, 54, ...
- From the multiples of 27, we have: 27, 54, 81, 108, ...
The common multiples in this case are: 27, 54, ...
- Identify the least common multiple
The least common multiple is the smallest number in the list of common multiples. Here, the smallest common multiple is:
$$ \text{LCM}(9, 27) = 27 $$
The least common multiple of 9 and 27 is ( \text{LCM}(9, 27) = 27 ).
More Information
The least common multiple (LCM) is especially useful in various mathematical applications, including adding and subtracting fractions with different denominators. The LCM also helps in solving problems related to periodic events, for example, determining when two events will coincide.
Tips
- Not listing enough multiples: It's important to ensure you've listed enough multiples to find all potential common multiples.
- Confusing LCM with GCD: Remember that LCM is about finding the smallest common multiple, while GCD (greatest common divisor) is about finding the largest number that divides both.
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