What is the LCM of 13 and 3?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 13 and 3. To solve this, we will identify the multiples of each number and find the smallest multiple that is common to both.

Answer

The least common multiple of 13 and 3 is $39$.

Steps to Solve

Identify the multiples of each number

First, we will list some of the multiples of 13 and 3.

Multiples of 13:
- $13 \times 1 = 13$
- $13 \times 2 = 26$
- $13 \times 3 = 39$
- $13 \times 4 = 52$
- $13 \times 5 = 65$
Multiples of 3:
- $3 \times 1 = 3$
- $3 \times 2 = 6$
- $3 \times 3 = 9$
- $3 \times 4 = 12$
- $3 \times 5 = 15$
- $3 \times 6 = 18$
- $3 \times 7 = 21$
- $3 \times 8 = 24$
- $3 \times 9 = 27$
- $3 \times 10 = 30$
- $3 \times 11 = 33$
- $3 \times 12 = 36$
- $3 \times 13 = 39$

Find the common multiples

Now we look for the least common multiple from the multiples listed.

From our lists:

The multiples of 13 are: 13, 26, 39, ...
The multiples of 3 are: 3, 6, 9, 12, ..., 39

The smallest number that appears in both lists is 39.

Conclusion

Therefore, the least common multiple (LCM) of 13 and 3 is $39$.

The least common multiple (LCM) of 13 and 3 is $39$.

More Information

The least common multiple is the smallest positive integer that is a multiple of both numbers. In this case, since 13 and 3 are relatively prime (they have no common factors other than 1), their LCM can also be calculated by the formula:

$$ LCM(a, b) = \frac{a \times b}{GCD(a, b)} $$

Where $GCD(a, b)$ is the greatest common divisor. For 13 and 3, $GCD(13, 3) = 1$, making the calculation straightforward.

Tips

Forgetting to list enough multiples may lead to missing the LCM.
Failing to check for common numbers in both lists can result in incorrect answers.

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