LCM of 12 and 13 is 156. 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 12 and 13. 156 is divisible by both 12 and 13 and it is the smallest common among the many common multiples. LCM is also called LCD, Least Common Divisor. You can refer to HCF and LCM to understand the difference.
What is LCM of 12 and 13
The Least Common Multiple or Lowest Common Multiple of 12 and 13 is 156.
How to Find LCM of 12 and 13?
LCM of 12 and 13 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 13 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 12 and 13 can be expressed as:
12 = 2 x 2 x 3
13 = 13 x 1
LCM (12, 13) = 2 x 2 x 3 x 13 = 156
LCM of 12 and 13 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 |
12 |
13 |
|
2 |
6 |
13 |
|
3 |
3 |
13 |
|
13 |
1 |
13 |
|
x |
1 |
1 |
Hence, LCM (12, 13) = 2 x 2 x 3 x 13 = 156
LCM of 12 and 13 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 12 and 13
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180.
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182.
LCM (12, 13) = 156
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 12 and 13?
Answer: 156 is the smallest number that is divisible by both 12 and 13.
What is the LCM for 1, 12 and 13?
Answer: LCM for 1, 12 and 13 is 156.
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