LCM of 109 and 114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 109 and 114 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 12426 as output. Here you can check the answer for Find the LCM of 109 and 114.
What is LCM of 109 and 114
Given Numbers are 109, 114
We can find the LCM of 109, 114 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 109 and 114
Multiples of 109 =109,218,327,436,545,654,763,872,981,1090,1199,1308,1417,1526,1635,1744,1853,
Multiples of 114 =114,228,342,456,570,684,798,912,1026,1140,1254,1368,1482,1596,1710,1824,1938,
Now, get the least common multiple of 109, 114 which is 12426
So, the LCM of 109, 114 is 12426.
Least Common Multiple (LCM) of 109 and 114 with the help of Prime Factorisation
One method for determining the LCM of 109 and 114 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 109's prime factorization:
| 109 | 109 |
| 1 |
Prime factors of 109 are 109.
109 = 1091
And this is 114's prime factorization:
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2, 3,19.
114 = 21×31×191
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:109, 2, 3,19
.21×31×191×1091 = 12426
This shows that the LCM of 109 and 114 is 12426.
How to Calculate the LCM of 109 and 114 Using Common Multiples
The first step in determining the Least Common Multiple of 109 and 114 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 109 and 114:
Lets look at the first ten multiples of these numbers, 109 and 114:
109,218,327,436,545,654,763,872,981,1853 are the first ten multiples of 109.
114,228,342,456,570,684,798,912,1026,1938 are the first ten multiples of 114.
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 109 and 114, for example, are 1308, 1853, and 1824. 12426 is the least common multiple since it is the smallest.
109 and 114 have an LCM of 12426.
Least Common Multiple of 109 and 114 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 109 and 114, than apply into the LCM equation.
GCF(109,114) = 1
LCM(109,114) = ( 109 × 114) / 1
LCM(109,114) = 12426 / 1
LCM(109,114) = 12426
Related Least Common Multiples of 109
Related Least Common Multiples of 114
Frequently Asked Questions on LCM of 109 and 114
1. What is the LCM of 109 and 114?
The LCM of 109 and 114 is 12426.
2. How to find the lowest common multiple of 109 and 114?
To find the lowest common multiple of 109 and 114, we have to get the multip;es of both numbers and identify the least common multiple in them which is 12426.
3. What are the Factors of 109?
Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.
4. What are the Factors of 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
5. How to Find the LCM of 109 and 114?Answer:
Least Common Multiple of 109 and 114 = 12426
Step 1: Find the prime factorization of 109
109 = 109
Step 2: Find the prime factorization of 114
114 = 2 x 3 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12426 = 2 x 3 x 19 x 109
Step 4: Therefore, the least common multiple of 109 and 114 is 12426.