LCM of 6 and 11 is 66. The value which evenly divides 6 and 11 gives the LCM value. Using the common multiples, the least common multiple of 6 and 11 can be found. The multiples of 6 are (6, 12, 18, 24, ….) and the multiples of 11 are (11, 22, 33, 44, 55, 66, ….) respectively. The methods we can make use of to get the LCM value are prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 6 and 11?
The answer to this question is 66. The LCM of 6 and 11 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 11, is the smallest positive integer 66 which is divisible by both 6 and 11 with no remainder.
How to Find LCM of 6 and 11?
LCM of 6 and 11 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 11 Using Prime Factorisation Method
The prime factorisation of 6 and 11, respectively, is given by:
6 = 2 x 3 = 2¹x 3¹
11 = 11¹
LCM (6, 11) = 66
LCM of 6 and 11 Using Division Method
We’ll divide the numbers (6, 11) by their prime factors to get the LCM of 6 and 11 using the division method (preferably common). The LCM of 6 and 11 is calculated by multiplying these divisors.
|
2 |
6 |
11 |
|
3 |
3 |
11 |
|
11 |
1 |
11 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (6, 11) = 66
LCM of 6 and 11 Using Listing the Multiples
To calculate the LCM of 6 and 11 by listing out the common multiples, list the multiples as shown below.
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ….
Multiples of 11 = 11, 22, 33, 44, 55, 66, …..
LCM (6, 11) = 66
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Video Lesson on Applications of LCM
LCM of 6 and 11 Solved Examples
Question: The LCM and GCD of two numbers are 66 and 1 respectively. If one number is 6, what is the other number?
Solution:
Consider the number as z
We know that
GCD x LCM = 6 x z
z = (GCD x LCM)/6
Substituting the values
z = (1 x 66)/6
z = 11
Hence, the other number is 11.
Frequently Asked Questions on LCM of 6 and 11
Calculate the GCF, if the LCM of 6 and 11 is 66
We know that
LCM x GCF = 6 x 11
As LCM (6, 11) is 66
66 x GCF = 66
GCF = 66/66 = 1
Determine the LCM of 6 and 11.
The LCM of 6 and 11 is 66. To find the LCM, the multiples of 6 and 11 has to be obtained
(6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ….) are the multiples of 6
(11, 22, 33, 44, 55, 66, …..) are the multiples of 11
The smallest multiple exactly divisible by 6 and 11 is 66.
Write the relation between GCF and LCM of 6 and 11.
The relation between GCF and LCM of 6 and 11 is
LCM x GCF = 6 x 11
LCM x GCF = 66
If the GCD and product of two numbers is 1 and 66, find the LCM.
Given
GCD = 1
Product = 66
LCM x GCD = Product
LCM = Product/GCD
LCM = 66/1 = 66
Hence, the LCM is 66.
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