LCM of 106 and 111
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 106 and 111 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 11766 as output. Here you can check the answer for Find the LCM of 106 and 111.
What is LCM of 106 and 111
Given Numbers are 106, 111
We can find the LCM of 106, 111 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 106 and 111
Multiples of 106 =106,212,318,424,530,636,742,848,954,1060,1166,1272,1378,1484,1590,1696,1802,
Multiples of 111 =111,222,333,444,555,666,777,888,999,1110,1221,1332,1443,1554,1665,1776,1887,
Now, get the least common multiple of 106, 111 which is 11766
So, the LCM of 106, 111 is 11766.
Least Common Multiple (LCM) of 106 and 111 with the help of Prime Factorisation
One method for determining the LCM of 106 and 111 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 111's prime factorization:
| 3 | 111 |
| 37 | 37 |
| 1 |
Prime factors of 111 are 3,37.
111 = 31×371
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, 3,37
.21×31×371×531 = 11766
This shows that the LCM of 106 and 111 is 11766.
How to Calculate the LCM of 106 and 111 Using Common Multiples
The first step in determining the Least Common Multiple of 106 and 111 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 106 and 111:
Lets look at the first ten multiples of these numbers, 106 and 111:
106,212,318,424,530,636,742,848,954,1802 are the first ten multiples of 106.
111,222,333,444,555,666,777,888,999,1887 are the first ten multiples of 111.
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 111, for example, are 1272, 1802, and 1776. 11766 is the least common multiple since it is the smallest.
106 and 111 have an LCM of 11766.
Least Common Multiple of 106 and 111 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 111, than apply into the LCM equation.
GCF(106,111) = 1
LCM(106,111) = ( 106 × 111) / 1
LCM(106,111) = 11766 / 1
LCM(106,111) = 11766
Related Least Common Multiples of 106
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 106 and 111
1. What is the LCM of 106 and 111?
The LCM of 106 and 111 is 11766.
2. How to find the lowest common multiple of 106 and 111?
To find the lowest common multiple of 106 and 111, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11766.
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 111?
Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.
5. How to Find the LCM of 106 and 111?Answer:
Least Common Multiple of 106 and 111 = 11766
Step 1: Find the prime factorization of 106
106 = 2 x 53
Step 2: Find the prime factorization of 111
111 = 3 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11766 = 2 x 3 x 37 x 53
Step 4: Therefore, the least common multiple of 106 and 111 is 11766.