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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

  1. 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:
    $15, 30, 45, 60, 75, 90, \ldots$

  2. 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.

  3. 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.

  4. 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.
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