What is the least common multiple of 9 and 4?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 4, which requires determining the smallest multiple that is common to both numbers.
Answer
36
Answer for screen readers
The final answer is 36
Steps to Solve
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Find Prime Factorization
Factorize each number into its prime factors:
- The prime factorization of 9: $9 = 3^2$
- The prime factorization of 4: $4 = 2^2$
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Identify the Highest Power of Each Prime
Determine the highest powers of each prime number that appear in any of the factorizations:
- For 2, the highest power is $2^2$
- For 3, the highest power is $3^2$
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Calculate the LCM
Multiply these highest powers together: $$ ext{LCM} = 2^2 imes 3^2 = 4 imes 9 = 36$$
The final answer is 36
More Information
The least common multiple (LCM) is useful in various areas of mathematics, including when adding or subtracting fractions with different denominators.
Tips
A common mistake is to simply multiply the numbers together without considering their prime factorizations. This method sometimes works, but not always.
