LCM of 14 and 22
LCM of 14 and 22 is the smallest number among all common multiples of 14 and 22. The first few multiples of 14 and 22 are (14, 28, 42, 56, 70, 84, 98, . . . ) and (22, 44, 66, 88, 110, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 22  by division method, by listing multiples, and by prime factorization.
1.  LCM of 14 and 22 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 22?
Answer: LCM of 14 and 22 is 154.
Explanation:
The LCM of two nonzero integers, x(14) and y(22), is the smallest positive integer m(154) that is divisible by both x(14) and y(22) without any remainder.
Methods to Find LCM of 14 and 22
Let's look at the different methods for finding the LCM of 14 and 22.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 14 and 22 by Listing Multiples
To calculate the LCM of 14 and 22 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 14 (14, 28, 42, 56, 70, 84, 98, . . . ) and 22 (22, 44, 66, 88, 110, . . . . )
 Step 2: The common multiples from the multiples of 14 and 22 are 154, 308, . . .
 Step 3: The smallest common multiple of 14 and 22 is 154.
∴ The least common multiple of 14 and 22 = 154.
LCM of 14 and 22 by Division Method
To calculate the LCM of 14 and 22 by the division method, we will divide the numbers(14, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 22.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 22. Write this prime number(2) on the left of the given numbers(14 and 22), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 22) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 14 and 22 is the product of all prime numbers on the left, i.e. LCM(14, 22) by division method = 2 × 7 × 11 = 154.
LCM of 14 and 22 by Prime Factorization
Prime factorization of 14 and 22 is (2 × 7) = 2^{1} × 7^{1} and (2 × 11) = 2^{1} × 11^{1} respectively. LCM of 14 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 7^{1} × 11^{1} = 154.
Hence, the LCM of 14 and 22 by prime factorization is 154.
☛ Also Check:
 LCM of 8 and 30  120
 LCM of 8 and 28  56
 LCM of 8 and 25  200
 LCM of 8 and 22  88
 LCM of 8 and 20  40
 LCM of 8 and 18  72
 LCM of 8 and 16  16
LCM of 14 and 22 Examples

Example 1: The product of two numbers is 308. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 308
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 308/2
Therefore, the LCM is 154.
The probable combination for the given case is LCM(14, 22) = 154. 
Example 2: Verify the relationship between GCF and LCM of 14 and 22.
Solution:
The relation between GCF and LCM of 14 and 22 is given as,
LCM(14, 22) × GCF(14, 22) = Product of 14, 22
Prime factorization of 14 and 22 is given as, 14 = (2 × 7) = 2^{1} × 7^{1} and 22 = (2 × 11) = 2^{1} × 11^{1}
LCM(14, 22) = 154
GCF(14, 22) = 2
LHS = LCM(14, 22) × GCF(14, 22) = 154 × 2 = 308
RHS = Product of 14, 22 = 14 × 22 = 308
⇒ LHS = RHS = 308
Hence, verified. 
Example 3: The GCD and LCM of two numbers are 2 and 154 respectively. If one number is 22, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 22 × y
⇒ y = (GCD × LCM)/22
⇒ y = (2 × 154)/22
⇒ y = 14
Therefore, the other number is 14.
FAQs on LCM of 14 and 22
What is the LCM of 14 and 22?
The LCM of 14 and 22 is 154. To find the least common multiple (LCM) of 14 and 22, we need to find the multiples of 14 and 22 (multiples of 14 = 14, 28, 42, 56 . . . . 154; multiples of 22 = 22, 44, 66, 88 . . . . 154) and choose the smallest multiple that is exactly divisible by 14 and 22, i.e., 154.
Which of the following is the LCM of 14 and 22? 15, 28, 11, 154
The value of LCM of 14, 22 is the smallest common multiple of 14 and 22. The number satisfying the given condition is 154.
If the LCM of 22 and 14 is 154, Find its GCF.
LCM(22, 14) × GCF(22, 14) = 22 × 14
Since the LCM of 22 and 14 = 154
⇒ 154 × GCF(22, 14) = 308
Therefore, the greatest common factor (GCF) = 308/154 = 2.
What is the Relation Between GCF and LCM of 14, 22?
The following equation can be used to express the relation between GCF and LCM of 14 and 22, i.e. GCF × LCM = 14 × 22.
How to Find the LCM of 14 and 22 by Prime Factorization?
To find the LCM of 14 and 22 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (22 = 2 × 11). LCM of 14 and 22 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 22.
⇒ LCM of 14, 22 = 2^{1} × 7^{1} × 11^{1} = 154.
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