LCM of 6, 12 and 14 is 84. Least Common Multiple or the Lowest common multiple is the full form for LCM. LCD which stands for Least Common Divisor and LCM are both same and are used interchangeably. LCM/LCD is the number that is a common multiple that is smallest in the group of common multiples, to the given set of numbers. Here the given set of numbers are 6, 12 and 14. The smallest common multiple for all these numbers among many is 84, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 6, 12 and 14
The Least Common Multiple or Lowest Common Multiple of 6, 12 and 14 is 84.
How to Find LCM of 6, 12 and 14?
LCM of 6, 12 and 14 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 12 and 14 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 6, 12 and 14 are represented as a product of prime factors. The union set of the prime factors with their product forms the LCM.
Here, 6, 12 and 14 can be expressed as;
6 = 2 × 3
12 = 2 × 2 × 3
14 = 2 × 7
LCM(6, 12 and 14) = 2 × 2 × 3 × 7 = 84
LCM of 6, 12 and 14 Using Division Method
In the Division Method, the given set of numbers are divided with the smallest prime number, till the remainder becomes 1. The product of these prime divisors, forms the LCM.
|
2 |
6 |
12 |
14 |
|
2 |
3 |
6 |
7 |
|
3 |
3 |
3 |
7 |
|
7 |
1 |
1 |
7 |
|
× |
1 |
1 |
1 |
LCM(6, 12 and 14) = 2 × 2 × 3 × 7 = 84
LCM of 6, 12 and 14 Using Listing the Multiples
By listing all the multiples, the first common multiple becomes the LCM.
Below is the list of multiples for 6, 12 and 14
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108
Multiples of 14
14, 28, 42, 56, 70, 84, 98, 112
LCM(6, 12 and 14) = 84
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 6, 12 and 14?
Answer: 84 is the smallest number that is divisible by 6, 12 and 14.
What is the LCM of 3 and 84?
Answer: LCM of 3 and 84 is 84 as 3 is the factor of 84.
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