Lowest common multiple of 6 and 8
Understand the Problem
The question is asking for the lowest common multiple (LCM) of the numbers 6 and 8. To find the LCM, we can use either the listing multiples method or the prime factorization method.
Answer
24
Answer for screen readers
The final answer is 24
Steps to Solve
- Find the prime factors of each number
Break down each number into its prime factors.
- For $6$: $6 = 2 imes 3$
- For $8$: $8 = 2 imes 2 imes 2$
- Determine the highest power of each prime number
Select the highest power of each prime factor from the prime factorizations.
- For $2$: The highest power is $2^3$
- For $3$: The highest power is $3$
- Multiply these highest powers to get the LCM
The LCM is obtained by multiplying the highest powers of all prime factors.
$$LCM(6, 8) = 2^3 imes 3 = 8 imes 3 = 24$$
Therefore, the LCM of $6$ and $8$ is $24$.
The final answer is 24
More Information
The LCM is the smallest number that both 6 and 8 can divide without a remainder. It is useful in adding, subtracting, or comparing fractions with different denominators.
Tips
A common mistake is not selecting the highest powers of all prime factors when calculating the LCM. Always list out the factorizations and pick the highest power for each prime to avoid errors.
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