What is the LCM of 6 and 30?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 6 and 30. To solve this, we find the multiples of each number and identify the smallest common multiple shared between them.
Answer
30
Answer for screen readers
The least common multiple (LCM) of 6 and 30 is 30.
Steps to Solve
- Identify the multiples of each number
First, we should list a few multiples of both numbers.
For 6, the multiples are: $$ 6, 12, 18, 24, 30, 36, 42, 48, \ldots $$
For 30, the multiples are: $$ 30, 60, 90, 120, \ldots $$
- Find the common multiples
Next, we need to identify the common multiples from the lists we have created. The smallest common multiple is what we're looking for.
Looking at our lists, we see that the common multiples of 6 and 30 includes: $$ 30, 60, 90, \ldots $$
- Select the least common multiple (LCM)
The smallest number that appears in both lists is 30. Thus, the least common multiple of 6 and 30 is: $$ \text{LCM}(6, 30) = 30 $$
The least common multiple (LCM) of 6 and 30 is 30.
More Information
The least common multiple is useful in various applications, including finding common denominators in fractions. Fun fact: The LCM of any number with 0 is always 0!
Tips
- Listing too few multiples and missing the correct common multiple. Ensure to check enough multiples.
- Confusing LCM with greatest common divisor (GCD). Remember, LCM is about finding the smallest shared multiple, while GCD finds the largest shared divisor.
