LCM of 14 and 22 is 154. The LCM is an important concept in Maths and has a wide range of applications in our day to day activities. Least common multiple of 14 and 22 is the smallest number we get from the common multiples. (14, 28, 42, 56, 70, 84, 98, ….) and (22, 44, 66, 88, 110, …..) are the first few multiples of 14 and 22. The LCM can be found using methods like division, prime factorisation and listing the multiples.
Also read: Least common multiple
What is LCM of 14 and 22?
The answer to this question is 154. The LCM of 14 and 22 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 14 and 22, is the smallest positive integer 154 which is divisible by both 14 and 22 with no remainder.
How to Find LCM of 14 and 22?
LCM of 14 and 22 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 22 Using Prime Factorisation Method
The prime factorisation of 14 and 22, respectively, is given by:
14 = 2 x 7 = 2¹ x 7¹
22 = 2 x 11 = 2¹ x 11¹
LCM (14, 22) = 154
LCM of 14 and 22 Using Division Method
We’ll divide the numbers (14, 22) by their prime factors to get the LCM of 14 and 22 using the division method (preferably common). The LCM of 14 and 22 is calculated by multiplying these divisors.
|
2 |
14 |
22 |
|
7 |
7 |
11 |
|
11 |
1 |
11 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (14, 22) = 154
LCM of 14 and 22 Using Listing the Multiples
To calculate the LCM of 14 and 22 by listing out the common multiples, list the multiples as shown below.
- Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, ….
- Multiples of 22 = 22, 44, 66, 88, 110, 132, 154,…..
The smallest common multiple of 14 and 22 is 154.
Therefore LCM (14, 22) = 154
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LCM of 14 and 22 Solved Examples
Question: The LCM and GCD of two numbers are 154 and 2. Find the other number when one number is 22.
Solution:
Consider y as the other number
GCD x LCM = 22 x y
y = (GCD x LCM)/22
y = (2 x 154)/22
y = 14
Hence, the LCM is 14.
Frequently Asked Questions on LCM of 14 and 22
Using the prime factorisation, determine the LCM of 14 and 22.
The LCM of 14 and 22 is 154.
Using the prime factorisation
14 = 2 x 7
22 = 2 x 11
LCM (14, 22) = 154
Write down the methods used to find the LCM of 14 and 22.
Find the LCM of 14 and 22 in 28, 15, 11 and 154.
If the product of two numbers is 308 and GCD is 2, find the LCM.
Given
Product = 308
GCD = 2
LCM x GCD = Product
LCM = Product/GCD
LCM = 308/2
LCM = 154
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