What is the 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 find the LCM, we need to consider the multiples of each number and determine the smallest value that is common among them.

Answer

The least common multiple (LCM) of 2, 3, and 6 is 6.

Steps to Solve

List the multiples of each number

Start by listing several multiples for each of the numbers 2, 3, and 6.

Multiples of 2: 2, 4, 6, 8, 10, 12, ...
Multiples of 3: 3, 6, 9, 12, 15, ...
Multiples of 6: 6, 12, 18, ...

Identify the common multiples

Now, look for the common multiples among the lists. The smallest numbers that appear in all lists (common multiples) are:

From the multiples of 2: 2, 4, 6, 8, 10, 12, ...
From the multiples of 3: 3, 6, 9, 12, ...
From the multiples of 6: 6, 12, ...

The common multiples are 6, 12, ...

Find the least common multiple (LCM)

The least common multiple is the smallest number that appears in all three lists. From the common multiples identified:

The smallest common multiple is 6.

The least common multiple (LCM) of 2, 3, and 6 is 6.

More Information

The LCM is useful in various applications, such as adding fractions with different denominators and solving problems that require synchronization of cycles, like scheduling events.

Tips

Relying solely on just one number's multiples without checking all given numbers for commonality.
Confusing LCM with the greatest common divisor (GCD), which is a different concept.

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