What is the least common multiple of 4 and 8

General
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what is the least common multiple of 4 and 8

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What is the least common multiple of 4 and 8?

The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both of those numbers. To find the LCM of 4 and 8, you can follow these steps:

Prime Factorization Method

  1. Prime Factorization

    • First, find the prime factorization of each number:
      • 4 = 2^2
      • 8 = 2^3

  2. Determine the Highest Power of Each Prime

    • List all the prime factors appearing in the factorizations while choosing the highest power of each.
      • The highest power of 2 appearing in the factorization is 2^3

  3. Multiply the Highest Powers Together

    • \text{LCM} = 2^3 = 8

Thus, the least common multiple (LCM) of 4 and 8 is 8.

Division Method

  1. List Multiples of Each Number

    • Multiples of 4: 4, 8, 12, 16, 20, 24, …
    • Multiples of 8: 8, 16, 24, 32, 40, 48, …

  2. Identify the Smallest Common Multiple

    • The smallest common multiple in both lists is 8.

Therefore, both methods confirm that the least common multiple (LCM) of 4 and 8 is 8.