What is the least common multiple (LCM) of 7 and 15?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 7 and 15. The LCM is the smallest number that is a multiple of both 7 and 15.
Answer
The least common multiple of 7 and 15 is $105$.
Answer for screen readers
The least common multiple of 7 and 15 is $105$.
Steps to Solve
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List the multiples of each number
Start by finding the first few multiples of both numbers.
For 7, the multiples are:
$7, 14, 21, 28, 35, 42, 49, 56, 63, 70, \ldots$
For 15, the multiples are:
$15, 30, 45, 60, 75, 90, \ldots$ -
Identify the common multiples
Now look for the numbers that appear in both lists of multiples.
From our earlier lists, we can see common multiples like:
$105, 210, 315, \ldots$
However, we are looking for the smallest one. -
Find the least common multiple (LCM)
The least common multiple is the smallest of the common multiples identified.
From our lists, we can see that $105$ is the first common multiple. -
Conclusion
Thus, the LCM of 7 and 15 is:
$$ \text{LCM}(7, 15) = 105 $$
The least common multiple of 7 and 15 is $105$.
More Information
The least common multiple (LCM) is useful in various mathematical applications, such as solving problems that involve adding or subtracting fractions with different denominators. The LCM helps determine a common base for calculations.
Tips
- A common mistake is to confuse LCM with the greatest common divisor (GCD). Remember, LCM is about finding the smallest common multiple, while GCD is about the largest common factor.
- Some may overlook checking beyond the immediate multiples or may only look for low multiples of both numbers, leading to an incorrect answer.
