🎧 New: AI-Generated Podcasts Turn your study notes into engaging audio conversations. Learn more

What is the lcm of 8 and 24?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 8 and 24. To find the LCM, we can list the multiples of each number and identify the smallest multiple they have in common, or use the prime factorization method.

Answer

$24$
Answer for screen readers

The least common multiple of 8 and 24 is $24$.

Steps to Solve

  1. List the multiples of each number

Start by listing the first few multiples of both 8 and 24.

  • Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
  • Multiples of 24: 24, 48, 72, 96, ...
  1. Identify the common multiples

Next, identify the common multiples from the lists made above. The common multiples of 8 and 24 are:

  • Common multiples: 24, 48, ...
  1. Find the least common multiple (LCM)

The least common multiple is the smallest number that appears in both lists of multiples. From the list, the smallest common multiple is:

$$ LCM(8, 24) = 24 $$

Alternatively, we can find the LCM using prime factorization:

  1. Prime factorization approach

Now we can also use prime factorization for each number:

  • Prime factorization of 8: $8 = 2^3$
  • Prime factorization of 24: $24 = 2^3 \times 3^1$

To find the LCM, take the highest power of each prime factor:

  • From both, we take $2^3$ and $3^1$.

So the LCM can also be calculated as:

$$ LCM(8, 24) = 2^3 \times 3^1 = 8 \times 3 = 24 $$

The least common multiple of 8 and 24 is $24$.

More Information

The least common multiple is important for solving problems involving multiples, particularly in fractions, as it helps in finding a common denominator. In this case, both methods (listing multiples and using prime factorization) led to the same result.

Tips

  • Failing to list enough multiples to find the least common multiple.
  • Confusing LCM with the greatest common divisor (GCD), which is a different concept.
Thank you for voting!
Use Quizgecko on...
Browser
Browser