LCM of 4 and 6
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 4 and 6. To solve this, we need to find the smallest number that is a multiple of both 4 and 6.
Answer
12
Answer for screen readers
The final answer is 12
Steps to Solve
- Find the prime factors of each number
First, we need to determine the prime factors of 4 and 6.
- The prime factors of 4 are $2 \times 2$.
- The prime factors of 6 are $2 \times 3$.
- Determine the highest power of each prime factor
To find the LCM, we take the highest power of each prime factor that appears in the factorizations.
- The highest power of 2 is $2^2$ from the number 4.
- The highest power of 3 is $3^1$ from the number 6.
- Multiply these highest powers together
The LCM is found by multiplying these highest powers: $$ ext{LCM}(4, 6) = 2^2 \times 3^1 = 4 \times 3 = 12$$
The final answer is 12
More Information
The least common multiple (LCM) is useful in problems that require the synchronization of cycles, such as in scheduling.
Tips
A common mistake is to incorrectly identify the highest power of each prime factor. Ensure that you carefully check the factorization of each number.
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