What is the least common multiple (LCM) of 6 and 13?
Understand the Problem
The question is asking to calculate the least common multiple (LCM) of the numbers 6 and 13. To solve this, we will identify the multiples of each number and find the smallest common multiple.
Answer
The least common multiple of 6 and 13 is $78$.
Answer for screen readers
The least common multiple of 6 and 13 is $78$.
Steps to Solve
- Identify the multiples of each number
List the first few multiples of 6 and 13.
Multiples of 6:
$6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, \ldots$
Multiples of 13:
$13, 26, 39, 52, 65, 78, 91, 104, 117, 130, \ldots$
- Look for the least common multiple
Find the smallest number that appears in both lists of multiples. From the lists above, the number $78$ is the first common multiple.
- Confirm it's the least common multiple
To ensure that $78$ is indeed the least common multiple, we can check if it is divisible by both numbers:
- For 6: $$\frac{78}{6} = 13$$ (which is an integer)
- For 13: $$\frac{78}{13} = 6$$ (which is also an integer)
Since $78$ is divisible by both, it is confirmed as the least common multiple.
The least common multiple of 6 and 13 is $78$.
More Information
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. In this case, $78$ is the first multiple that 6 and 13 have in common.
Tips
A common mistake is not listing enough multiples of each number or simply assuming a common multiple without verifying divisibility. Always double-check that the identified LCM is divisible by both original numbers.
