what is the lowest common multiple of 4 and 8
What is the lowest common multiple of 4 and 8?
Answer: To find the Lowest Common Multiple (LCM) of two numbers, we need to identify the smallest number that is a multiple of both numbers. Here are the detailed steps to find the LCM of 4 and 8:
1. Prime Factorization:
First, let’s find the prime factorization of each number:
-
4: The prime factorization of 4 is (2^2).
4 = 2 \times 2 = 2^2 -
8: The prime factorization of 8 is (2^3).
8 = 2 \times 2 \times 2 = 2^3
2. Identify the Highest Power of Each Prime:
To find the LCM, we take the highest power of each prime number that appears in the factorization.
- For prime number 2, the highest power is (2^3) (since 3 > 2).
3. Calculate the LCM:
Now, we multiply the highest power of each prime factor.
\text{LCM} = 2^3
Calculating this, we get:
2^3 = 8
Conclusion:
The lowest common multiple of 4 and 8 is 8.
Therefore, the LCM of 4 and 8 is (\boxed{8}).
This makes sense because 8 is a multiple of both 4 and 8, and there is no smaller number that is a common multiple of both.