LCM of 3, 4, and 7
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3, 4, and 7. To find the LCM, we need to determine the smallest number that is a multiple of all three numbers.
Answer
The least common multiple (LCM) of 3, 4, and 7 is $84$.
Answer for screen readers
The least common multiple (LCM) of 3, 4, and 7 is 84.
Steps to Solve
- List the multiples of each number
First, we find the multiples of each number separately.
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ...
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
- Multiples of 7: 7, 14, 21, 28, 35, 42, ...
- Identify the common multiples
Next, we look for numbers that appear in all three lists.
From the lists above, the common multiples of 3, 4, and 7 are: 84, 168, ...
- Select the least common multiple
From the common multiples identified, the smallest one is the least common multiple (LCM).
The least common multiple is:
$$ \text{LCM}(3, 4, 7) = 84 $$
The least common multiple (LCM) of 3, 4, and 7 is 84.
More Information
The least common multiple is the smallest positive integer that is divisible by each of the given numbers. In this case, 84 is the first number that is a multiple of 3, 4, and 7. Interestingly, the LCM is often used in various applications, including finding common denominators in fractions.
Tips
- Stopping too early: Sometimes, students stop finding multiples before getting to the smallest common one. Make sure to check more multiples if needed.
- Misidentifying the smallest multiple: It's easy to mistakenly pick a larger common multiple instead of the least. Always verify that it's the smallest one.
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