What is the LCM of 8 and 12?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 8 and 12. To find the LCM, we can list the multiples of each number and identify the smallest multiple that is common to both lists.
Answer
24
Answer for screen readers
The LCM of 8 and 12 is 24.
Steps to Solve
- Prime factorization of each number
To start, we perform a prime factorization of each number:
- The prime factorization of 8 is $8 = 2^3$
- The prime factorization of 12 is $12 = 2^2 imes 3^1$
- Identify the highest power of each prime factor
The LCM is found by taking the highest power of each prime factor present in the factorization:
- The highest power of 2 present is $2^3$
- The highest power of 3 present is $3^1$
- Multiply these highest powers together
We then multiply these factors together to get the LCM: $$\text{LCM} = 2^3 imes 3^1 = 8 imes 3 = 24$$
- Write down the final answer
The LCM of 8 and 12 is 24.
The LCM of 8 and 12 is 24.
More Information
The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers. It ensures that the multiples are both covered with the least amount of repetition.
Tips
A common mistake is to confuse LCM with the Greatest Common Divisor (GCD). LCM focuses on the highest powers of all primes involved, while GCD focuses on the lowest powers.
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