LCM of 2, 3, and 6
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 2, 3, and 6. To solve this, we will identify the multiples of each number and find the smallest multiple that all numbers share.
Answer
The least common multiple of 2, 3, and 6 is $6$.
Answer for screen readers
The least common multiple (LCM) of the numbers 2, 3, and 6 is $6$.
Steps to Solve
- List the multiples of each number
Start by identifying the first few multiples of each number:
- For 2: $2, 4, 6, 8, 10, 12, \ldots$
- For 3: $3, 6, 9, 12, 15, \ldots$
- For 6: $6, 12, 18, \ldots$
- Identify the common multiples
Next, look for the multiples that appear in all lists. The multiples for each number are:
- 2: $2, 4, 6, 8, 10, 12, \ldots$
- 3: $3, 6, 9, 12, 15, \ldots$
- 6: $6, 12, 18, \ldots$
The common multiples are $6, 12, \ldots$
- Find the least common multiple
The least common multiple is the smallest common value from the lists. Here, the smallest common multiple is $6$.
The least common multiple (LCM) of the numbers 2, 3, and 6 is $6$.
More Information
The least common multiple (LCM) is useful in problems involving fractions, ratio comparisons, and scheduling events. In this case, since 6 is a multiple of both 2 and 3, it represents the smallest number that can be evenly divided by all of them.
Tips
A common mistake is to overlook one of the multiples when listing them or to assume a number must be a multiple of all three without checking. To avoid this, make sure to list enough multiples for each number and check for commonality.
