What is the LCM of 2, 3, and 5?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 2, 3, and 5. To find the LCM, we need to determine the smallest number that is a multiple of all three numbers.
Answer
The least common multiple of 2, 3, and 5 is $30$.
Answer for screen readers
The least common multiple of 2, 3, and 5 is 30.
Steps to Solve
- List the multiples of each number
Start by listing several multiples of each number to find the common multiples.
- Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, ...
- Identify the common multiples
Look through the lists and find the common multiples shared among 2, 3, and 5.
From the lists:
- The common multiples are: 30, 60, 90, ...
- Determine the least common multiple
The least common multiple is the smallest common multiple found in the previous step.
Among the common multiples, the smallest one is:
$$ \text{LCM}(2, 3, 5) = 30 $$
The least common multiple of 2, 3, and 5 is 30.
More Information
The least common multiple (LCM) is particularly useful in problems involving fractions, where you need a common denominator. The LCM can also be applied in finding cycles or patterns in number sets.
Tips
- Not listing enough multiples: Sometimes people don't create sufficient multiples for the numbers, which may lead to missing common multiples.
- Misidentifying smallest common multiple: It's important to ensure that when identifying the LCM, you select the smallest one from the common multiples found.
