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 find the LCM, we look for the smallest number that is a multiple of both 9 and 6.
Answer
18
Answer for screen readers
The final answer is 18
Steps to Solve
- Find the prime factors of each number
Prime factorization is breaking down a number into its prime number multipliers.
For 9: $$9 = 3^2$$
For 6: $$6 = 2 imes 3$$
- Identify the highest power of all prime numbers involved
We take the highest power of each prime factor involved.
For prime number 2: highest power is $$2^1$$
For prime number 3: highest power is $$3^2$$
- Multiply these highest powers together
The LCM is found by multiplying these highest powers together:
$$LCM = 2^1 imes 3^2$$
- Calculate the LCM
Now calculate the result:
$$LCM = 2 imes 9 = 18$$
The final answer is 18
More Information
The least common multiple (LCM) of two numbers is the smallest multiple that both numbers share. It's useful in various applications such as finding common periods and solving problems involving shared work rates.
Tips
A common mistake when finding the LCM is not identifying the highest power of each prime factor correctly. Make sure to compare the powers of each prime number between the two numbers and use the highest one.
