LCM of 12 and 21 is 84. Why is 84 the LCM of 12 and 21? Why not 85? Or 83? As the acronym LCM suggests it is the least or smallest or the first common multiple that is common to both 12 and 21. LCM stands for Least Common multiple or Lowest common multiple. LCM is also called LCD, Least Common Divisor. You can use the LCM for more details.
What is LCM of 12 and 21
The Least Common Multiple or Lowest Common Multiple of 12 and 21 is 84.
How to Find LCM of 12 and 21?
LCM of 12 and 21 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 21 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 12 and 21 can be expressed as;
12 = 2 x 2 x 3
21 = 3 x 7
LCM (12, 21) = 2 x 2 x 3 x 7 = 84
LCM of 12 and 21 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.
|
3 |
12 |
21 |
|
2 |
4 |
7 |
|
2 |
2 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
Hence, LCM (12, 21) = 2 x 2 x 3 x 7 = 84
LCM of 12 and 21 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 21
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108.
Multiples of 21: 21, 42, 63, 84, 105, 126..
LCM (12, 21) = 84
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 12 and 21?
Answer: 84 is the smallest number that is divisible by both 12 and 21.
What is the LCM for 3, 12 and 21?
Answer: LCM for 3, 12 and 21 is 84.
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