What is the lcm of 3 and 8

General
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what is the lcm of 3 and 8

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What is the LCM of 3 and 8?

Answer: To find the Least Common Multiple (LCM) of 3 and 8, follow these steps:

1. Prime Factorization:

  • Determine the prime factorizations of the given numbers.
    • The prime factorization of 3 is:
      3 = 3^1
    • The prime factorization of 8 is:
      8 = 2^3

2. Identify the Highest Powers:

  • Identify the highest powers of all prime numbers appearing in the factorizations.
    • For prime number 2, the highest power is 2^3.
    • For prime number 3, the highest power is 3^1.

3. Calculate the LCM:

  • Multiply the highest powers of all prime factors together to get the LCM.
    \text{LCM} = 2^3 \times 3^1
    • Calculate:
      2^3 = 8
      3^1 = 3
    • Therefore:
      \text{LCM} = 8 \times 3 = 24

Conclusion:

The Least Common Multiple (LCM) of 3 and 8 is 24.