What is the LCM of 8 and 12?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 8 and 12. To find the LCM, we can list the multiples of each number and identify the smallest multiple that is common to both lists.

Answer

24
Answer for screen readers

The LCM of 8 and 12 is 24.

Steps to Solve

  1. Prime factorization of each number

To start, we perform a prime factorization of each number:

  • The prime factorization of 8 is $8 = 2^3$
  • The prime factorization of 12 is $12 = 2^2 imes 3^1$
  1. Identify the highest power of each prime factor

The LCM is found by taking the highest power of each prime factor present in the factorization:

  • The highest power of 2 present is $2^3$
  • The highest power of 3 present is $3^1$
  1. Multiply these highest powers together

We then multiply these factors together to get the LCM: $$\text{LCM} = 2^3 imes 3^1 = 8 imes 3 = 24$$

  1. Write down the final answer

The LCM of 8 and 12 is 24.

The LCM of 8 and 12 is 24.

More Information

The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers. It ensures that the multiples are both covered with the least amount of repetition.

Tips

A common mistake is to confuse LCM with the Greatest Common Divisor (GCD). LCM focuses on the highest powers of all primes involved, while GCD focuses on the lowest powers.

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