LCM of 12 and 9
Understand the Problem
The question is asking to calculate the least common multiple (LCM) of the numbers 12 and 9. The LCM is the smallest positive integer that is divisible by both numbers.
Answer
36
Answer for screen readers
The final answer is 36
Steps to Solve
- Find the prime factorization of each number
Prime factorize each given number.
- 12: $12 = 2^2 imes 3^1$
- 9: $9 = 3^2$
- Identify the highest powers of all prime factors
Select the highest powers of all prime factors from the factorizations.
- For 2: The highest power is $2^2$
- For 3: The highest power is $3^2$
- Multiply these highest powers to get the LCM
Multiply the identified highest powers of all prime factors.
$$LCM(12, 9) = 2^2 imes 3^2 = 4 imes 9 = 36$$
The final answer is 36
More Information
The LCM is useful in solving problems related to adding, subtracting, or comparing fractions with different denominators.
Tips
A common mistake is to multiply the numbers directly instead of finding the highest powers of the prime factors. Always ensure to use the highest power of each prime factor.
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