LCM of 3, 6, and 9
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3, 6, and 9. To find the LCM, we will look for the smallest multiple that is common among these three numbers.
Answer
$18$
Answer for screen readers
The least common multiple (LCM) of 3, 6, and 9 is $18$.
Steps to Solve
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List the multiples of each number
We will start by listing some of the multiples for each number.
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Multiples of 3:
$$ 3, 6, 9, 12, 15, 18, 21, 24, 27, \ldots $$ -
Multiples of 6:
$$ 6, 12, 18, 24, 30, \ldots $$ -
Multiples of 9:
$$ 9, 18, 27, 36, \ldots $$
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Identify the common multiples
Next, we will find the common multiples from the lists we created.
From the lists:
- The common multiples are:
$$ 18, 36, \ldots $$
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Determine the least common multiple
The least common multiple (LCM) is the smallest number that appears in all three lists.
From our common multiples, the smallest is:
$$ \text{LCM} = 18 $$
The least common multiple (LCM) of 3, 6, and 9 is $18$.
More Information
The least common multiple is particularly useful when adding or subtracting fractions with different denominators, as it can help in finding a common denominator.
Tips
- Not Listing Enough Multiples: Sometimes, students may not list enough multiples to find the least common multiple. Always ensure you have enough multiples to identify the common ones.
- Confusing LCM with GCD: Remember that LCM is about finding the smallest shared multiple, while GCD (greatest common divisor) is about finding the largest shared factor.
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