Least common multiple of 11 and 10

Understand the Problem

The question is asking us to find the least common multiple (LCM) of the numbers 11 and 10. This involves identifying the smallest number that is a multiple of both given numbers.

Answer

The least common multiple of 11 and 10 is $110$.

Steps to Solve

List the multiples of each number

First, we list the multiples of both numbers (11 and 10) to find the common multiples:
- Multiples of 11: $11, 22, 33, 44, 55, 66, 77, 88, 99, 110, \ldots$
- Multiples of 10: $10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, \ldots$
Identify the common multiples

Next, we look for the common multiples from both lists. The first common multiple we find is:
- 110
Determine the least common multiple

Since 110 is the first number that appears in both lists, we can confirm that:

The least common multiple (LCM) of 11 and 10 is: $$ \text{LCM}(11, 10) = 110 $$

The least common multiple (LCM) of 11 and 10 is $110$.

More Information

The least common multiple (LCM) represents the smallest number that is a multiple of both integers. In this case, 110 is significant because it is the first number that both 11 and 10 can divide evenly, making it useful in many mathematical applications, such as adding fractions with different denominators.

Tips

Forgetting to list enough multiples: Ensure that you list enough multiples to catch the common ones.
Confusing LCM with GCD: Remember that the least common multiple is different from the greatest common divisor (GCD).

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