LCM of 12 and 84 is 84. LCM is Least Common Multiple or Lowest Common Multiple. Consider the example for finding the LCM of 12 and 84. The answer is 84. 84 is divisible by both 12 and 84. Even 168 is divisible by 12 and 84, however it is not the LCM for 12 and 84. The smaller number than 168 is 84 which is divisible by both 12 and 84. Hence 84 is the Least Common Multiple for 12 and 84. You can use the Prime Factorization and Division method to find the LCM.
What is LCM of 12 and 84
The Least Common Multiple or Lowest Common Multiple of 12 and 84 is 84.
How to Find LCM of 12 and 84?
LCM of 12 and 84 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 84 Using Prime Factorisation Method
In the Prime Factorization method, the given numbers 12 and 84 are expressed as the product of prime factors;
12 = 2 × 2 × 3
84 = 2 × 2 × 3 × 7
Here (2 × 2 × 3) is common to both 12 and 84. This is multiplied with 7 to get the LCM.
Hence, LCM (12, 84) = 2 × 2 × 3 × 7 = 84
LCM of 12 and 84 Using Division Method
In the Division Method, the numbers 12 and 84 are divided by the smallest prime divisors. The division is done until no more division can be done or only when prime numbers are remaining.
The product of the prime divisors forms the LCM.
|
2 |
12 |
84 |
|
2 |
6 |
42 |
|
3 |
3 |
21 |
|
7 |
1 |
7 |
|
× |
1 |
1 |
Hence, LCM (12, 84) = 2 × 2 × 3 × 7 = 84
LCM of 12 and 84 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 84;
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108
Multiples of 84
84, 168, 252
LCM (12, 18) = 84
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 12 and 84?
Answer: 84 is the smallest number that is divisible by both 12 and 84.
What is the LCM for 2, 4, 12 and 84?
Answer: LCM for 2, 4, 12 and 84 is 84 as 2 and 4 both are the factors of 12 and 84.
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