What is the LCM of 6, 10, and 15?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 6, 10, and 15. To solve this, we will determine the multiples of each number and find the smallest multiple that is common to all three.

Answer

$30$

Steps to Solve

List the multiples of each number

To find the LCM, we first need to list some multiples of each number:

Multiples of 6: $6, 12, 18, 24, 30, 36, 42, 48, 54, 60, \ldots$
Multiples of 10: $10, 20, 30, 40, 50, 60, 70, \ldots$
Multiples of 15: $15, 30, 45, 60, 75, \ldots$

Identify the common multiples

Next, we identify the multiples that are common among the three lists. The common multiples from the lists above are:

$30, 60, \ldots$

Select the least common multiple

From the common multiples found, the smallest one is the LCM. Therefore, the least common multiple of 6, 10, and 15 is:

$$ \text{LCM}(6, 10, 15) = 30 $$

The least common multiple of 6, 10, and 15 is $30$.

More Information

The least common multiple is significant in various mathematical applications, including solving problems involving fractions, ratios, and scheduling events that occur at different intervals. The LCM helps in finding a common timeframe or constraint.

Tips

Forgetting to list enough multiples may lead to missing the least common multiple.
Not checking all three numbers for commonality which can result in an incorrect answer.

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