lcm 9 12
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 12. To solve this, we will determine the multiples of both numbers and find the smallest one that they share.
Answer
$36$
Answer for screen readers
The least common multiple of 9 and 12 is $36$.
Steps to Solve
- List the Multiples of Each Number
First, we need to determine the multiples of both 9 and 12.
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The multiples of 9 are: $$ 9, 18, 27, 36, 45, 54, \dots $$
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The multiples of 12 are: $$ 12, 24, 36, 48, 60, \dots $$
- Identify Common Multiples
Next, we will look for the common multiples from the lists above. From our lists, we see:
- Common multiples of 9 and 12 are: $$ 36, 72, 108, \dots $$
- Determine the Least Common Multiple
Finally, we pick the smallest common multiple, which is:
$$ \text{LCM}(9, 12) = 36 $$
The least common multiple of 9 and 12 is $36$.
More Information
The least common multiple (LCM) is a fundamental concept in number theory. It is useful in solving problems related to ratios, fractions, and finding common denominators. The LCM of two numbers can also be found using prime factorization or the relationship between GCF and LCM: $$ \text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCF}(a, b)} $$
Tips
- Skipping the part where all multiples are listed and just guessing. It’s important to list them out to ensure no common multiples are missed.
- Not distinguishing between "least" and "greatest" common multiples. Ensure you are looking for the smallest one.
