What is the least common multiple of 60 and 15?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 60 and 15. To find the LCM, we will look for the smallest number that is a multiple of both 60 and 15.
Answer
The least common multiple of 60 and 15 is \( 60 \).
Answer for screen readers
The least common multiple of 60 and 15 is ( \text{LCM}(60, 15) = 60 ).
Steps to Solve
- List the multiples of each number
Start by listing the multiples of each number until you find the smallest common multiple.
- Multiples of 60: 60, 120, 180, 240, ...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
- Identify the common multiples
Now we check which numbers appear in both lists of multiples.
- The common multiples of 60 and 15 are: 60, 120, ...
- Determine the least common multiple
From the list of common multiples, the smallest one is the least common multiple (LCM).
- The least common multiple of 60 and 15 is 60.
The least common multiple of 60 and 15 is ( \text{LCM}(60, 15) = 60 ).
More Information
The least common multiple is useful in various mathematical applications, such as adding fractions with different denominators. In this case, since 60 is a multiple of 15, it is also the LCM.
Tips
- A common mistake is not listing enough multiples to find the LCM. Make sure to list enough terms.
- Some may confuse the LCM with the greatest common divisor (GCD). Remember that LCM is the smallest common multiple, while GCD is the largest common divisor.
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