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lcm of 6 and 27

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 6 and 27. To find this, we can identify the multiples of each number and determine the smallest multiple they have in common.

Answer

The least common multiple of 6 and 27 is $54$.
Answer for screen readers

The least common multiple of 6 and 27 is $54$.

Steps to Solve

  1. Find the Multiples of Each Number

    First, list the multiples of 6 and 27.

    • Multiples of 6: $6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, \ldots$

    • Multiples of 27: $27, 54, 81, 108, 135, 162, 189, \ldots$

  2. Identify Common Multiples

    Next, find the common multiples between the two lists.

    From the above lists, the common multiples are: $54, 108, \ldots$

  3. Determine the Least Common Multiple

    The smallest number in the common multiples list is the LCM.

    Thus, the least common multiple of 6 and 27 is: $$ \text{LCM}(6, 27) = 54 $$

The least common multiple of 6 and 27 is $54$.

More Information

The least common multiple (LCM) is the smallest number that is a multiple of both numbers. Finding the LCM can also be done using prime factorization or the formula $\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}$, where GCD is the greatest common divisor.

Tips

  • Forgetting to include all multiples: When listing multiples, it’s important to ensure enough multiples are listed to identify common ones.
  • Assuming the first multiple is always the LCM: The LCM is specifically the smallest common multiple, so be careful not to confuse it with any common multiple.
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