LCM of 6 and 11
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 6 and 11 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 66 as output. Here you can check the answer for Find the LCM of 6 and 11.
What is LCM of 6 and 11
Given Numbers are 6, 11
We can find the LCM of 6, 11 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 6 and 11
Multiples of 6 =6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,
Multiples of 11 =11,22,33,44,55,66,77,88,99,110,121,132,143,154,165,176,187,
Now, get the least common multiple of 6, 11 which is 66
So, the LCM of 6, 11 is 66.
Least Common Multiple (LCM) of 6 and 11 with the help of Prime Factorisation
One method for determining the LCM of 6 and 11 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 6's prime factorization:
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 6 are 2,3.
6 = 21×31
And this is 11's prime factorization:
| 11 | 11 |
| 1 |
Prime factors of 11 are 11.
11 = 111
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: 2,3,11
.21×31×111 = 66
This shows that the LCM of 6 and 11 is 66.
How to Calculate the LCM of 6 and 11 Using Common Multiples
The first step in determining the Least Common Multiple of 6 and 11 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 6 and 11:
Lets look at the first ten multiples of these numbers, 6 and 11:
6,12,18,24,30,36,42,48,54,102 are the first ten multiples of 6.
11,22,33,44,55,66,77,88,99,187 are the first ten multiples of 11.
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 6 and 11, for example, are 72, 102, and 176. 66 is the least common multiple since it is the smallest.
6 and 11 have an LCM of 66.
Least Common Multiple of 6 and 11 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 11, than apply into the LCM equation.
GCF(6,11) = 1
LCM(6,11) = ( 6 × 11) / 1
LCM(6,11) = 66 / 1
LCM(6,11) = 66
Related Least Common Multiples of 6
Related Least Common Multiples of 11
Frequently Asked Questions on LCM of 6 and 11
1. What is the LCM of 6 and 11?
The LCM of 6 and 11 is 66.
2. How to find the lowest common multiple of 6 and 11?
To find the lowest common multiple of 6 and 11, we have to get the multip;es of both numbers and identify the least common multiple in them which is 66.
3. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
4. What are the Factors of 11?
Answer: Factors of 11 are 1, 11. There are 2 integers that are factors of 11. The greatest factor of 11 is 11.
5. How to Find the LCM of 6 and 11?Answer:
Least Common Multiple of 6 and 11 = 66
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 11
11 = 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 66 = 2 x 3 x 11
Step 4: Therefore, the least common multiple of 6 and 11 is 66.