What is the least common multiple of 8 and 4

General
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what is the least common multiple of 8 and 4

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What is the least common multiple of 8 and 4?

Answer: To find the least common multiple (LCM) of two numbers, 8 and 4, follow these steps:

Step-by-Step Solution:

1. Prime Factorization:

  • Find the prime factors for both numbers.
    • ( 8 = 2^3 )
    • ( 4 = 2^2 )

2. Identify the Highest Powers of Each Prime Factor:

  • For the prime number 2, the highest power that appears in the factorizations is ( 2^3 ).

3. Calculate the LCM:

  • The LCM is found by taking the highest powers of all prime factors present in the numbers.
  • Therefore, LCM of 8 and 4 is 2^3 = 8

Conclusion:

The least common multiple (LCM) of 8 and 4 is \boxed{8}

Explanation:

The concept of LCM is useful for finding the smallest multiple that two or more numbers share. In this case, since 4 divides evenly into 8, the smallest number that is a multiple of both 8 and 4 is simply 8. This finding aligns with our mathematical approach using prime factorization and ensures that both numbers can divide into the LCM without a remainder.