What is the LCM of 6, 12, and 15?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 6, 12, and 15. To find the LCM, we will determine the smallest number that is a multiple of all three numbers.
Answer
The least common multiple (LCM) of 6, 12, and 15 is $60$.
Answer for screen readers
The least common multiple (LCM) of 6, 12, and 15 is $60$.
Steps to Solve
- List the multiples of each number
Start by listing the multiples of each number given in the problem.
Multiples of 6:
$$ 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96,... $$
Multiples of 12:
$$ 12, 24, 36, 48, 60, 72, 84, 96,... $$
Multiples of 15:
$$ 15, 30, 45, 60, 75, 90, 105, 120,... $$
- Identify the common multiples
Next, we look for the common multiples from the lists we created.
The common multiples of 6, 12, and 15 from our lists are:
$$ 60, 120, 180, ... $$
- Choose the smallest common multiple
From the common multiples identified, select the smallest one.
The smallest common multiple is:
$$ 60 $$
The least common multiple (LCM) of 6, 12, and 15 is $60$.
More Information
The least common multiple (LCM) is useful in various mathematical applications, such as adding fractions with different denominators and solving problems involving ratios. The LCM of a set of numbers is the smallest number that is a multiple of all of them, making it an essential concept in both algebra and number theory.
Tips
- Forgetting to list enough multiples: Some may stop after a few multiples. Ensure to check multiple lists thoroughly to find common values.
- Confusing LCM with GCD: The least common multiple is often mixed up with the greatest common divisor. Remember that LCM is about finding the smallest shared multiple, while GCD is the greatest shared factor.
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