LCM of 106 and 114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 106 and 114 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 6042 as output. Here you can check the answer for Find the LCM of 106 and 114.
What is LCM of 106 and 114
Given Numbers are 106, 114
We can find the LCM of 106, 114 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 106 and 114
Multiples of 106 =106,212,318,424,530,636,742,848,954,1060,1166,1272,1378,1484,1590,1696,1802,
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 106, 114 which is 6042
So, the LCM of 106, 114 is 6042.
Least Common Multiple (LCM) of 106 and 114 with the help of Prime Factorisation
One method for determining the LCM of 106 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 106's prime factorization:
| 2 | 106 |
| 53 | 53 |
| 1 |
Prime factors of 106 are 2,53.
106 = 21×531
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: 2,53, 3,19
.21×31×191×531 = 6042
This shows that the LCM of 106 and 114 is 6042.
How to Calculate the LCM of 106 and 114 Using Common Multiples
The first step in determining the Least Common Multiple of 106 and 114 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 106 and 114:
Lets look at the first ten multiples of these numbers, 106 and 114:
106,212,318,424,530,636,742,848,954,1802 are the first ten multiples of 106.
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 106 and 114, for example, are 1272, 1802, and 1824. 6042 is the least common multiple since it is the smallest.
106 and 114 have an LCM of 6042.
Least Common Multiple of 106 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 106 and 114, than apply into the LCM equation.
GCF(106,114) = 2
LCM(106,114) = ( 106 × 114) / 2
LCM(106,114) = 12084 / 2
LCM(106,114) = 6042
Related Least Common Multiples of 106
Related Least Common Multiples of 114
Frequently Asked Questions on LCM of 106 and 114
1. What is the LCM of 106 and 114?
The LCM of 106 and 114 is 6042.
2. How to find the lowest common multiple of 106 and 114?
To find the lowest common multiple of 106 and 114, we have to get the multip;es of both numbers and identify the least common multiple in them which is 6042.
3. What are the Factors of 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
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 106 and 114?Answer:
Least Common Multiple of 106 and 114 = 6042
Step 1: Find the prime factorization of 106
106 = 2 x 53
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 = 6042 = 2 x 3 x 19 x 53
Step 4: Therefore, the least common multiple of 106 and 114 is 6042.