What is the least common multiple of 7 and 15?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 7 and 15. To find the LCM, we need to determine the smallest multiple that both numbers share.
Answer
The least common multiple of 7 and 15 is $105$.
Answer for screen readers
The least common multiple (LCM) of 7 and 15 is $105$.
Steps to Solve
- List the multiples of each number We start by listing the multiples of 7 and 15.
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The multiples of 7 are: $7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...$
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The multiples of 15 are: $15, 30, 45, 60, 75, 90, ...$
- Identify common multiples Next, we identify the common multiples from the lists obtained in the previous step.
The common multiples of 7 and 15 are: $105, 210, 315, ...$
- Determine the least common multiple From the common multiples, we identify the least one.
The least common multiple (LCM) of 7 and 15 is: $$ 105 $$
The least common multiple (LCM) of 7 and 15 is $105$.
More Information
The LCM is useful in various applications such as finding common denominators in fraction addition and solving problems involving synchronization of cycles like scheduling.
Tips
- Not listing enough multiples: Sometimes students stop too early in listing the multiples. Make sure to check that you've found the least common multiple.
- Confusing LCM with GCD: Remember that LCM refers to the least common multiple, while GCD (greatest common divisor) is the largest number that divides both.
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