LCM of 8 and 12 is 24. LCM also known as Least Common multiple or Lowest common multiple is the smallest or the least positive integer that is divisible by the given set of numbers. Consider the example for finding the LCM of 8 and 12. The answer is 24. 24 is divisible by both 8 and 12. Even 48 is divisible by 8 and 12, however it is not the LCM for 8 and 12. The smaller number than 48 is 24 which is divisible by both 8 and 12. Hence 24 is the Least Common Multiple for 8 and 12. You can refer to LCM for more information.
What is LCM of 8 and 12
The Least Common Multiple or Lowest Common Multiple of 8 and 12 is 24.
How to Find LCM of 8 and 12?
LCM of 8 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 12 Using Prime Factorisation Method
We can write 8 and 12 as the product of prime numbers, such that;
8 = 2 x 2 x 2
12 = 2 x 2 x 3
LCM (8, 12) = 2 x 2 x 2 x 3 = 24
LCM of 8 and 12 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
| 2 | 8 | 12 |
| 2 | 4 | 6 |
| 2 | 2 | 3 |
| 3 | 1 | 3 |
| x | 1 | 1 |
LCM (8, 12) = 2 x 2 x 2 x 3 = 24
LCM of 8 and 12 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 8 and 12
| Multiples of 8 | Multiples of 12 |
| 8 | 12 |
| 16 | 24 |
| 24 | 36 |
| 32 | 48 |
LCM (8, 12) = 24
Related Articles
Video Lesson on Applications of LCM
Solved Examples
- What is the smallest number that is divisible by both 8 and 12?
Answer: 24 is the smallest number that is divisible by both 8 and 12.
2. Two school buses arrive every 8 and 12 minutes at the school ground. At what time in minutes do both buses arrive together at the playground?
Answer: At the 24th minute, both the buses arrive together at the playground. This is a problem to find out the least common multiple of 8 and 12 and hence the answer is 24.
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