LCM of 3 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3 and 13. The LCM is the smallest positive integer that is a multiple of both numbers. To find the LCM, we can list the multiples of each number or use the prime factorization method.
Answer
$39$
Answer for screen readers
The least common multiple of 3 and 13 is $39$.
Steps to Solve
- Identify the multiples of each number
First, list the multiples of both numbers.
For 3:
- 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, ...
For 13:
- 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ...
- Find the common multiples
Next, find the common multiples from both lists above.
From our lists:
- The common multiples of 3 and 13 are 39, 78, 117, etc.
- Determine the least common multiple
The least common multiple is the smallest number from the common multiples found, which in this case is 39.
The least common multiple of 3 and 13 is $39$.
More Information
The least common multiple (LCM) is useful in many areas of mathematics, including fractions and algebra. Since 3 and 13 are both prime, their LCM can also be found by multiplying them together.
Tips
- A common mistake is to choose non-common multiples instead of finding the smallest one. Always ensure to identify the least common multiple specifically.
- Another mistake could be to overlook that both numbers may be prime, making their LCM simply their product.
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