LCM of 6 and 22 is 66. The number divisible exactly by the given numbers is the LCM value. Least common multiple of 6 and 22 is the number we get using the common multiples. (6, 12, 18, 24, 30, ….) and (22, 44, 66, 88, 110, 132,….) are the few multiples of 6 and 22. Learn to find the LCM using various methods like prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 6 and 22?
The answer to this question is 66. The LCM of 6 and 22 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 22, is the smallest positive integer 66 which is divisible by both 6 and 22 with no remainder.
How to Find LCM of 6 and 22?
LCM of 6 and 22 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 22 Using Prime Factorisation Method
The prime factorisation of 6 and 22, respectively, is given by:
6 = 2 × 3 = 2¹× 3¹
22 = 2 × 11 = 2¹× 11¹
LCM (6, 22) = 66
LCM of 6 and 22 Using Division Method
We’ll divide the numbers (6, 22) by their prime factors to get the LCM of 6 and 22 using the division method (preferably common). The LCM of 6 and 22 is calculated by multiplying these divisors.
|
2 |
6 |
22 |
|
3 |
3 |
11 |
|
11 |
1 |
11 |
|
× |
1 |
1 |
No further division can be done.
Hence, LCM (6, 22) = 66
LCM of 6 and 22 Using Listing the Multiples
To calculate the LCM of 6 and 22 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 22 = 22, 44, 66, 88, 110, 132, ……
The smallest common multiple of 6 and 22 is 66.
Therefore LCM (6, 22) = 66
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LCM of 6 and 22 Solved Examples
Question: The LCM and GCD of two numbers are 66 and 2. If one number is 22, find the other number.
Solution:
Consider m as the other number
GCD × LCM = 22 × m
m = (GCD × LCM)/22
m = (2 × 66)/22
m = 6
Hence, the other number is 6.
Frequently Asked Questions on LCM of 6 and 22
How can we find the LCM of 6 and 22?
List the methods used to get the LCM value of 6 and 22.
Find the GCF if the LCM of 6 and 22 is 66.
LCM × GCF = 6 × 22
Given
LCM of 6 and 22 = 66
66 × GCF = 132
GCF = 132/66 = 2
What is the LCM of 6 and 22?
Find the LCM if the GCD is 2 and the product of two numbers is 132.
Given
GCD = 2
Product = 132
LCM × GCD = Product of two numbers
LCM = Product/GCD
LCM = 132/2 = 66
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