What is the LCM of 6 and 4?
Understand the Problem
The question is asking us to calculate the least common multiple (LCM) of the numbers 6 and 4. To solve this, we will find the smallest number that is a multiple of both 6 and 4.
Answer
12
Answer for screen readers
The final answer is 12
Steps to Solve
- Find the prime factorizations of 6 and 4
Prime factorization of 6: $$6 = 2 \times 3$$
Prime factorization of 4: $$4 = 2^2$$
- Identify the highest power of each prime number
We take the highest power of each prime that appears in the factorizations:
- The highest power of 2 that appears is $2^2$
- The highest power of 3 that appears is $3^1$
- Multiply these highest powers to find the LCM
LCM = highest power of 2 imes highest power of 3 $$\text{LCM} = 2^2 \times 3 = 4 \times 3 = 12$$
The final answer is 12
More Information
The LCM of two numbers is the smallest number that both original numbers divide into without leaving any remainder. In this case, 12 is the smallest number that both 6 and 4 divide into.
Tips
A common mistake is to incorrectly identify the highest powers of the prime factors. Make sure to double-check the prime factorization of each number.
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