What is the LCM of 9 and 6?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 6. To solve this, we will first find the prime factors of each number, then determine the highest powers of each prime factor involved, and finally multiply those together to get the LCM.
Answer
18
Answer for screen readers
The final answer is 18
Steps to Solve
- Prime factorization of each number
Find the prime factors of 9 and 6:
- $9 = 3^2$
- $6 = 2 \times 3$
- Determine the highest powers of each prime factor
Identify the highest power of each prime number involved:
- Highest power of 2: $2^1$
- Highest power of 3: $3^2$
- Multiply the highest powers together
Multiply these highest powers to get the LCM:
$$ \text{LCM} = 2^1 \times 3^2 = 18 $$
The final answer is 18
More Information
The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both numbers. For 9 and 6, it turns out to be 18.
Tips
A common mistake is to forget to take the highest power of all primes involved. Always ensure you have the highest power of each prime factor.