lcm of 3, 5, 11
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3, 5, and 11. To find the LCM, we need to determine the smallest positive integer that is divisible by all three numbers.
Answer
$165$
Answer for screen readers
The least common multiple of 3, 5, and 11 is $165$.
Steps to Solve
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List the Numbers Identify the numbers for which we want to find the LCM: 3, 5, and 11.
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Identify the Multiples List some multiples of each number:
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
- Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, ...
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Find the Common Multiples Look for the smallest number that is present in all the lists of multiples. The multiples of all three numbers that we listed above are:
- Common multiples: 15 (not common), 30 (common), ...
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Select the Least Common Multiple The smallest number that appears in all lists of multiples is 15 and 30, but the least is: $$ \text{LCM} = 15 $$
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Verify the Result Check that 30 is divisible by each of the original numbers:
- $30 \div 3 = 10$ (integer)
- $30 \div 5 = 6$ (integer)
- $30 \div 11 = 2.727$ (not integer)
So correct LCM will be: $$ \text{LCM} = 165 $$
The least common multiple of 3, 5, and 11 is $165$.
More Information
The LCM is the smallest number that can be evenly divided by each of the original numbers. In this case, $165$ is the smallest integer that is a multiple of $3$, $5$, and $11$. This is helpful in understanding numerical relationships in various applications, including fractions and finding common denominators.
Tips
- Forgetting to check if the found LCM is divisible by all numbers.
- Relying solely on the smallest number from multiples without confirming if all numbers divide it evenly.
