What is the least common multiple of 9 and 4?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 9 and 4, which requires determining the smallest multiple that is common to both numbers.

Answer

36
Answer for screen readers

The final answer is 36

Steps to Solve

  1. Find Prime Factorization

    Factorize each number into its prime factors:

    • The prime factorization of 9: $9 = 3^2$
    • The prime factorization of 4: $4 = 2^2$
  2. Identify the Highest Power of Each Prime

    Determine the highest powers of each prime number that appear in any of the factorizations:

    • For 2, the highest power is $2^2$
    • For 3, the highest power is $3^2$
  3. Calculate the LCM

    Multiply these highest powers together: $$ ext{LCM} = 2^2 imes 3^2 = 4 imes 9 = 36$$

The final answer is 36

More Information

The least common multiple (LCM) is useful in various areas of mathematics, including when adding or subtracting fractions with different denominators.

Tips

A common mistake is to simply multiply the numbers together without considering their prime factorizations. This method sometimes works, but not always.

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