LCM of 16 and 22 is 176. From the multiples of 16 and 22, the value divisible exactly indicates the LCM. Least common multiple of 16 and 22 is the common multiple of two numbers we get using the multiplication operation. (16, 32, 48, 64, 80, 96, 112, ….) and (22, 44, 66, 88, 110, ….) are the multiples of 16 and 22. The LCM of two numbers can be determined using various methods like the listing of multiples, prime factorization and division.
Also read: Least common multiple
What is LCM of 16 and 22?
The answer to this question is 176. The LCM of 16 and 22 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 16 and 22, is the smallest positive integer 176 which is divisible by both 16 and 22 with no remainder.
How to Find LCM of 16 and 22?
LCM of 16 and 22 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16 and 22 Using Prime Factorisation Method
The prime factorisation of 16 and 22, respectively, is given by:
16 = 2 x 2 x 2 x 2 = 2⁴
22 = 2 x 11 = 2¹ x 11¹
LCM (16, 22) = 176
LCM of 16 and 22 Using Division Method
We’ll divide the numbers (16, 22) by their prime factors to get the LCM of 16 and 22 using the division method (preferably common). The LCM of 16 and 22 is calculated by multiplying these divisors.
|
2 |
16 |
22 |
|
2 |
8 |
11 |
|
2 |
4 |
11 |
|
2 |
2 |
11 |
|
11 |
1 |
11 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (16, 22) = 176
LCM of 16 and 22 Using Listing the Multiples
To calculate the LCM of 16 and 22 by listing out the common multiples, list the multiples as shown below:
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, . . . .
Multiples of 22 = 22, 44, 66, 88, 110, 132, 154, 176, 198, 220, . . . .
LCM (16, 22) = 176
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 16 and 22 Solved Examples
Question: If the GCD is 2 and the product of two numbers is 352, find the LCM.
Solution:
Given,
GCD = 2
Product = 352
LCM x GCD = Product
LCM = Product/GCD
LCM = 352/2
LCM = 176
Hence, the LCM of 16 and 22 is 176.
Frequently Asked Questions on LCM of 16 and 22
What are the methods used to find the LCM of 16 and 22?
The methods used to find the LCM of 16 and 22 are:
Prime Factorisation
Division method
Listing the multiples
Using the prime factorisation method, determine the LCM of 16 and 22.
We should first know the factors to determine the LCM
16 = 2 x 2 x 2 x 2
22 = 2 x 11
LCM is the product of prime factors raised to the highest exponent among 16 and 22.
LCM of 16 and 22 = 176
Find the GCF if the LCM of 16 and 22 is 176.
LCM x GCF = 16 x 22
As the LCM = 176
176 x GCF = 352
GCF = 352/176 = 2
Show the relation between LCM and GCF of 16 and 22.
The relation between LCM and GCF of 16 and 22 is
GCF x LCM = 16 x 22
GCF x LCM = 352
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