What is the LCM of 30 and 6?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 30 and 6. To find it, we will determine the multiples of each number and identify the smallest common one.
Answer
$30$
Answer for screen readers
The least common multiple (LCM) of 30 and 6 is $30$.
Steps to Solve
- Identify the multiples of 30 and 6
First, we will list some of the multiples of both numbers.
-
Multiples of 30: $$30, 60, 90, 120, 150, ...$$
-
Multiples of 6: $$6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...$$
- Find the common multiples
Next, we look for the smallest number that appears in both lists.
From the lists:
- The common multiples are $$30, 60, ...$$
- Determine the least common multiple (LCM)
The least common multiple is the smallest number that appears in both lists of multiples.
Since the common multiples we identified are $$30, 60,...$$
The LCM of 30 and 6 is $$30$$.
The least common multiple (LCM) of 30 and 6 is $30$.
More Information
The least common multiple is a crucial concept in number theory that is often used in problems involving fractions and ratios. It helps find a common denominator for adding or subtracting fractions.
Tips
- Listing too few multiples or skipping some of them can lead to incorrect conclusions. Be thorough.
- Confusing the least common multiple with the greatest common divisor (GCD). Remember that LCM is the smallest common multiple, while GCD is the largest factor they share.
