lcm of 12 and 42
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 12 and 42. To find the LCM, we will determine the multiples of both numbers and identify the smallest multiple that is common to both.
Answer
$84$
Answer for screen readers
The least common multiple (LCM) of 12 and 42 is $84$.
Steps to Solve
- List the multiples of each number
Start by listing the multiples of 12 and 42.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, ...
Multiples of 42: 42, 84, 126, 168, 210, 252, 294, ...
- Identify the common multiples
Next, look for the multiples that are common in both lists:
From the multiples listed, we can see that both lists share: 84, 168, ...
- Determine the least common multiple
Now, the least common multiple is the smallest number that appears in both lists.
The smallest number found is 84.
The least common multiple (LCM) of 12 and 42 is $84$.
More Information
The least common multiple is a crucial concept used in many areas of mathematics, particularly in fraction simplification and in problems involving multiple cycles occurring simultaneously, like timed events.
Tips
- Some might fail to list enough multiples to find the LCM.
- Others may not check all common multiples and assume they have found the LCM too early.
- It is also common to confuse LCM with the greatest common divisor (GCD).
