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
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Find the Multiples of Each Number
First, list the multiples of 6 and 27.
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Multiples of 6: $6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, \ldots$
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Multiples of 27: $27, 54, 81, 108, 135, 162, 189, \ldots$
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Identify Common Multiples
Next, find the common multiples between the two lists.
From the above lists, the common multiples are: $54, 108, \ldots$
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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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