lcm of 3, 5, and 10
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3, 5, and 10. To solve this, we will identify the multiples of each number and find the smallest multiple that all three numbers share.
Answer
30
Answer for screen readers
The least common multiple of 3, 5, and 10 is 30.
Steps to Solve
- Identify the multiples of each number
First, let's find the multiples of each number:
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
- The multiples of 5 are: 5, 10, 15, 20, 25, 30, ...
- The multiples of 10 are: 10, 20, 30, 40, ...
- List the multiples until we find a common one
Now, let's list out the multiples until we find a common multiple:
- For 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- For 5: 5, 10, 15, 20, 25, 30
- For 10: 10, 20, 30
- Find the least common multiple
The smallest number that appears in all three lists of multiples is 30. Thus, the least common multiple (LCM) of 3, 5, and 10 is:
$$ \text{LCM}(3, 5, 10) = 30 $$
The least common multiple of 3, 5, and 10 is 30.
More Information
The least common multiple (LCM) is the smallest positive integer that is divisible by each of the given numbers. It is often used in problems involving adding and comparing fractions, conversions, and scheduling events.
Tips
- Failing to list a sufficient number of multiples can cause you to miss the LCM.
- Confusing LCM with the greatest common divisor (GCD); remember that LCM is about multiples while GCD focuses on common factors.
