LCM of 12 and 22 is 132. The smallest number which is evenly divisible by the multiples of the 12 and 22 is the LCM. By writing the multiples of the given two numbers, the least common multiple of 12 and 22 can be found. (12, 24, 36, 48, 60, 72, ….) and (22, 44, 66, 88, 110, 132,….) are the multiples of 12 and 22. The LCM of 12 and 22 as per the prime factorisation method, division method and listing the multiples are given here in a comprehensive manner.
Also read: Least common multiple
What is LCM of 12 and 22?
The answer to this question is 132. The LCM of 12 and 22 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 22, is the smallest positive integer 132 which is divisible by both 12 and 22 with no remainder.
How to Find LCM of 12 and 22?
LCM of 12 and 22 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 22 Using Prime Factorisation Method
The prime factorisation of 12 and 22, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
22 = 2 x 11 = 2¹ x 11¹
LCM (12, 22) = 132
LCM of 12 and 22 Using Division Method
We’ll divide the numbers (12, 22) by their prime factors to get the LCM of 12 and 22 using the division method (preferably common). The LCM of 12 and 22 is calculated by multiplying these divisors.
|
2 |
12 |
22 |
|
2 |
6 |
11 |
|
3 |
3 |
11 |
|
11 |
1 |
11 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (12, 22) = 132
LCM of 12 and 22 Using Listing the Multiples
To calculate the LCM of 12 and 22 by listing out the common multiples, list the multiples as shown below
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, . . . .
Multiples of 22 = 22, 44, 66, 88, 110, 132, . . . .
LCM (12, 22) = 132
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LCM of 12 and 22 Solved Examples
Question: If the GCD is 2 and the product of two numbers is 264, find the LCM.
Solution:
Given
GCD = 2
Product = 264
LCM x GCD = Product
LCM = Product/GCD
LCM = 264/2 = 132
Hence, the LCM is 132.
Frequently Asked Questions on LCM of 12 and 22
What is the LCM of 12 and 22?
List the methods which can be used to get the LCM value of 12 and 22.
What is the GCF if the LCM of 12 and 22 is 132?
LCM x GCF = 12 x 22
Given
LCM of 12 and 22 = 132
132 x GCF = 264
GCF = 264/132 = 2
Show the relation between GCF and LCM of 12 and 22.
The relation between GCF and LCM of 12 and 22 is
GCF x LCM = 12 x 22
GCF x LCM = 264
Using prime factorisation, find the LCM of 12 and 22.
Using prime factorisation,
12 = 2 x 2 x 3
22 = 2 x 11
LCM of 12 and 22 is 132.
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