LCM of 12 and 14
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 12 and 14 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 84 as output. Here you can check the answer for Find the LCM of 12 and 14.
What is LCM of 12 and 14
Given Numbers are 12, 14
We can find the LCM of 12, 14 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 12 and 14
Multiples of 12 =12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,
Multiples of 14 =14,28,42,56,70,84,98,112,126,140,154,168,182,196,210,224,238,
Now, get the least common multiple of 12, 14 which is 84
So, the LCM of 12, 14 is 84.
Least Common Multiple (LCM) of 12 and 14 with the help of Prime Factorisation
One method for determining the LCM of 12 and 14 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 12's prime factorization:
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 12 are 2,3.
12 = 22×31
And this is 14's prime factorization:
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 14 are 2,7.
14 = 21×71
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,7
.22×31×71 = 84
This shows that the LCM of 12 and 14 is 84.
How to Calculate the LCM of 12 and 14 Using Common Multiples
The first step in determining the Least Common Multiple of 12 and 14 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 12 and 14:
Lets look at the first ten multiples of these numbers, 12 and 14:
12,24,36,48,60,72,84,96,108,204 are the first ten multiples of 12.
14,28,42,56,70,84,98,112,126,238 are the first ten multiples of 14.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 12 and 14, for example, are 144, 204, and 224. 84 is the least common multiple since it is the smallest.
12 and 14 have an LCM of 84.
Least Common Multiple of 12 and 14 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 14, than apply into the LCM equation.
GCF(12,14) = 2
LCM(12,14) = ( 12 × 14) / 2
LCM(12,14) = 168 / 2
LCM(12,14) = 84
Related Least Common Multiples of 12
Related Least Common Multiples of 14
Frequently Asked Questions on LCM of 12 and 14
1. What is the LCM of 12 and 14?
The LCM of 12 and 14 is 84.
2. How to find the lowest common multiple of 12 and 14?
To find the lowest common multiple of 12 and 14, we have to get the multip;es of both numbers and identify the least common multiple in them which is 84.
3. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
4. What are the Factors of 14?
Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.
5. How to Find the LCM of 12 and 14?Answer:
Least Common Multiple of 12 and 14 = 84
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 14
14 = 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 84 = 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 12 and 14 is 84.