What is the LCM of 10 and 60?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 10 and 60. To find the LCM, we can identify the multiples of both numbers and find the smallest multiple that is common to both.
Answer
The least common multiple of 10 and 60 is $60$.
Answer for screen readers
The least common multiple of 10 and 60 is $60$.
Steps to Solve
- List out the multiples of each number
We need to find the multiples of 10 and 60.
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The multiples of 10 are: $$10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...$$
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The multiples of 60 are: $$60, 120, 180, 240, ...$$
- Identify the common multiples
Next, we look for the numbers that are common in the lists of multiples we created.
From our lists, the common multiples are: $$60, 120, 180, ...$$
- Determine the least common multiple (LCM)
The smallest common multiple from our list is: $$60$$
Thus, the least common multiple of 10 and 60 is 60.
The least common multiple of 10 and 60 is $60$.
More Information
The least common multiple is a key concept in number theory and is useful in various applications, such as finding common denominators in fraction addition. The LCM of two numbers is the smallest positive integer that is divisible by both numbers.
Tips
- Not listing enough multiples: Sometimes, students stop listing too early or miss important numbers. It's crucial to list enough to find the common ones.
- Miscounting: Double-check counts when identifying multiples or assuming a number is a multiple without confirming.
