LCM of 11 and 6 is 66. LCM can be defined as the smallest common multiple of two or more numbers. Students can clear their doubts regarding the LCM concept by referring to the article Least Common Multiple (LCM) formulated by the subject experts. Following this article on a regular basis, students improve their abilities to solve complex problems asked in exams with ease. Learn how to calculate the least common multiple of 11 and 6 with the help of solved examples and FAQs here.
What is LCM of 11 and 6?
The Least Common Multiple of 11 and 6 is 66.
How to Find LCM of 11 and 6?
LCM of 11 and 6 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 11 and 6 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree.
11 = 11
6 = 2 × 3
LCM (11, 6) = 11 × 6 = 66
LCM of 11 and 6 Using Division Method
In the division method, to determine the least common multiple of 11 and 66, we divide the numbers 11 and 6 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 11 and 6.
| 2 | 11 | 6 |
| 3 | 11 | 3 |
| 11 | 11 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (11, 6) = 2 × 3 × 11 = 66
LCM of 11 and 6 Using Listing the Multiples
In this method, we list the multiples of 11 and 6 to find the least common multiple among them. Let us glance at the multiples of 11 and 6 given below.
Multiples of 11: 11, 22, 33, 44, 55, 66, …………….
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, …………..
LCM (11, 6) = 66
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 11 and 6?
Solution: 66 is the smallest number that is divisible by both 11 and 6.
2. What is the LCM if the product of two numbers is 66 and their GCD is 1?
Solution: Given
Product of numbers = 66
GCD = 1
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 66 / 1
LCM = 66
Therefore the LCM is 66.
Frequently Asked Questions on LCM of 11 and 6
What is the LCM of 11 and 6?
Is the LCM of 11 and 6 the same as the HCF of 11 and 6?
Name the methods used to find the least common multiple of 11 and 6.
The methods used to find the least common multiple of 11 and 6 are:
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 11 and 6 is 66?
GCF × LCM = 11 × 6
Given
LCM = 66
GCF × 66 = 11 × 6
GCF = 1
Calculate the LCM of 11 and 6 using prime factorisation.
In prime factorisation, we express the numbers as the product of prime factors to determine the LCM
11 = 11
6 = 2 × 3
LCM (11, 6) = 11 × 2 × 3 = 66
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