lcm of 3 and 9
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 3 and 9. We will determine the smallest multiple that is common to both numbers.
Answer
9
Answer for screen readers
The final answer is 9
Steps to Solve
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Find the prime factors of each number
- For 3, the prime factorization is $3 = 3^1$.
- For 9, the prime factorization is $9 = 3^2$.
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Identify the highest power of each prime number
- The prime number here is 3.
- The highest power of 3 in the prime factorizations is $3^2$.
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Calculate the LCM using the highest powers
- The LCM is the product of the highest powers of all prime numbers.
- Here, the LCM is $3^2 = 9$.
The final answer is 9
More Information
One interesting way to look at it is that since 9 is a multiple of 3, the smallest multiple that both share is 9.
Tips
Sometimes, people mistakenly think the LCM of two numbers is just their product. That's only true if the numbers are coprime (i.e., their greatest common divisor is 1).
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