The least common multiple (LCM) of the numbers 6, 12, and 11 is 132.
To find the LCM, we can approach it by identifying the multiples of each number and finding the smallest multiple that they all share.
First, let’s list the multiples of each number:
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, …
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, …
- Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, …
Now, we can see that the first multiple that appears in all three lists is 132. Therefore, the least common multiple of 6, 12, and 11 is 132.
This number is significant because it is the smallest number that all three original numbers divide into without leaving a remainder. This makes the LCM useful in various applications, including solving problems involving fractions and finding common time intervals.