lcm of 13 and 6
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 13 and 6. To solve this, we need to identify the multiples of both numbers and determine the smallest multiple that they share.
Answer
$78$
Answer for screen readers
The least common multiple of 13 and 6 is $78$.
Steps to Solve
- Identify the multiples of the numbers
List the multiples of each number.
For 13: $$ 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, \ldots $$
For 6: $$ 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, \ldots $$
- Find the common multiples
Look for the smallest number that appears in both lists of multiples.
From the list above, the common multiples are: $$ 78, 156, \ldots $$
- Identify the least common multiple (LCM)
The least common multiple is the smallest number that is common in both sets of multiples, which is:
$$ \text{LCM}(13, 6) = 78 $$
The least common multiple of 13 and 6 is $78$.
More Information
The least common multiple (LCM) is useful in various applications such as finding common denominators in fractions or solving problems involving cycles, where two or more events repeat at different intervals.
Tips
- Forgetting to list enough multiples leading to missing the correct LCM.
- Confusing LCM with the greatest common divisor (GCD); remember that LCM is the smallest common multiple, while GCD is the largest common factor.
