least common multiple of 12 and 42
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 12 and 42. To solve it, we will look for the smallest positive integer that is a multiple of both 12 and 42.
Answer
The least common multiple of 12 and 42 is $84$.
Answer for screen readers
The least common multiple of 12 and 42 is $84$.
Steps to Solve
- List the multiples of each number
First, we need to find the multiples of both 12 and 42.
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
- Multiples of 42: 42, 84, 126, 168, ...
- Identify the common multiples
Next, we look for the smallest number that appears in both lists of multiples. From the lists above, the common multiples are:
- 84, 168, ...
- Determine the least common multiple
The least common multiple (LCM) is the smallest of the common multiples we found.
Thus, the LCM of 12 and 42 is 84.
The least common multiple of 12 and 42 is $84$.
More Information
The least common multiple is the smallest number that is a multiple of both original numbers. In this case, $84$ can be divided evenly by both $12$ and $42$. It's also interesting that the LCM can be found using the prime factorization method or the formula using the greatest common divisor (GCD).
Tips
- Not listing enough multiples: Make sure to list plenty of multiples to ensure you find the LCM.
- Not identifying the smallest common multiple: Sometimes, larger common multiples are mistakenly chosen. Always check for the smallest one.
