lcm of 2 and 11
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 2 and 11. To solve this, we find the smallest number that is a multiple of both 2 and 11.
Answer
$22$
Answer for screen readers
The least common multiple of 2 and 11 is $22$.
Steps to Solve
- Identify the multiples of each number
List the multiples of 2:
- 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, ...
List the multiples of 11:
- 11, 22, 33, 44, 55, ...
- Find the smallest common multiple
Look at the lists of multiples found in the previous step. The smallest number that appears in both lists is the least common multiple (LCM).
- From the multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, ...
- From the multiples of 11: 11, 22, 33, ...
- Determine the least common multiple
The smallest number that appears in both lists is 22. Therefore, the least common multiple of 2 and 11 is: $$ \text{LCM}(2, 11) = 22 $$
The least common multiple of 2 and 11 is $22$.
More Information
The least common multiple (LCM) is useful in various applications, especially in determining common denominators in fractions. In this case, since 2 and 11 are prime numbers, their LCM is simply their product.
Tips
- A common mistake is thinking that the LCM of two numbers is always the result of dividing their product by their greatest common divisor (GCD) without checking that the GCD is 1.
- Another mistake is failing to list enough multiples to identify the smallest common multiple.
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