least common multiple of 3 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3 and 13. To solve this, we will identify the smallest positive integer that is a multiple of both 3 and 13.
Answer
The least common multiple of 3 and 13 is 39.
Answer for screen readers
The least common multiple of 3 and 13 is 39.
Steps to Solve
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Identify the multiples of each number
Start by listing the multiples of 3 and 13.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
Multiples of 13: 13, 26, 39, 52, 65, 78, ... -
Find the smallest common multiple
Now, look for the smallest number that appears in both lists of multiples.
From the lists above, we can see that the first common multiple is 39. -
Conclusion
Thus, the least common multiple (LCM) of 3 and 13 is 39.
The least common multiple of 3 and 13 is 39.
More Information
The least common multiple is useful in various applications including finding common denominators in fractions. Since 3 and 13 are both prime numbers, their LCM can be calculated by simply multiplying them together, which gives $3 \times 13 = 39$.
Tips
- Mistake: Confusing LCM with greatest common divisor (GCD).
To avoid this, remember that LCM is the smallest common multiple, while GCD is the largest number that divides both.
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