lcm of 24 and 42
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 24 and 42. To find this, we will determine the multiples of both numbers and identify the smallest multiple they share.
Answer
$168$
Answer for screen readers
The least common multiple (LCM) of 24 and 42 is $168$.
Steps to Solve
- List the multiples of each number
To find the LCM, we first list out some multiples of both numbers.
For 24, the first few multiples are:
$$ 24, 48, 72, 96, 120, 144, 168, 192, \ldots $$
For 42, the first few multiples are:
$$ 42, 84, 126, 168, 210, \ldots $$
- Identify the common multiples
Next, we look for the smallest number that appears in both lists.
The common multiples of 24 and 42 include:
$$ 168, 336, \ldots $$
- Determine the least common multiple (LCM)
From the common multiples, the least common multiple is the smallest one.
Thus, the least common multiple of 24 and 42 is:
$$ LCM(24, 42) = 168 $$
The least common multiple (LCM) of 24 and 42 is $168$.
More Information
The least common multiple helps to find a common time space for events that occur at different intervals. In this case, 168 is the smallest number into which both 24 and 42 can fit evenly, meaning both 24 and 42 will align at this multiple.
Tips
- Focusing solely on the first few multiples may lead to missing the least common multiple. It is important to consider enough multiples to ensure you find the LCM.
- Not organizing or clearly identifying the common multiples could lead to confusion. Keeping the lists accessible and clear helps in comparing them.
