Find the LCM of 12 and 18.
Understand the Problem
The question is asking us to find the least common multiple (LCM) of the two numbers 12 and 18. The LCM is the smallest number that is a multiple of both 12 and 18.
Answer
The least common multiple of 12 and 18 is $36$.
Answer for screen readers
The least common multiple of 12 and 18 is $36$.
Steps to Solve
- List the multiples of each number
First, we need to find the multiples of 12 and 18.
For 12, the first few multiples are: $$ 12, 24, 36, 48, 60, 72, \ldots $$
For 18, the first few multiples are: $$ 18, 36, 54, 72, 90, \ldots $$
- Identify the common multiples
Now, we look for the numbers that appear in both lists of multiples. The common multiples of 12 and 18 are: $$ 36, 72, \ldots $$
- Find the least common multiple
The least of the common multiples is: $$ \text{LCM}(12, 18) = 36 $$
The least common multiple of 12 and 18 is $36$.
More Information
The least common multiple (LCM) can be useful in various applications, especially in adding or subtracting fractions with different denominators. Also, the LCM can be calculated using prime factorization, which can be another approach to verify the result.
Tips
- Forgetting to look for additional multiples. It's important to check enough multiples to ensure you find the LCM.
- Confusing LCM with greatest common divisor (GCD). They are different concepts; remember that LCM finds the smallest common multiple, while GCD finds the largest common factor.
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