LCM of 14 and 122
LCM of 14 and 122 is the smallest number among all common multiples of 14 and 122. The first few multiples of 14 and 122 are (14, 28, 42, 56, 70, 84, 98, . . . ) and (122, 244, 366, 488, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 122  by listing multiples, by prime factorization, and by division method.
1.  LCM of 14 and 122 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 122?
Answer: LCM of 14 and 122 is 854.
Explanation:
The LCM of two nonzero integers, x(14) and y(122), is the smallest positive integer m(854) that is divisible by both x(14) and y(122) without any remainder.
Methods to Find LCM of 14 and 122
Let's look at the different methods for finding the LCM of 14 and 122.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 14 and 122 by Division Method
To calculate the LCM of 14 and 122 by the division method, we will divide the numbers(14, 122) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 122.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 122. Write this prime number(2) on the left of the given numbers(14 and 122), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 122) 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 122 is the product of all prime numbers on the left, i.e. LCM(14, 122) by division method = 2 × 7 × 61 = 854.
LCM of 14 and 122 by Listing Multiples
To calculate the LCM of 14 and 122 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 122 (122, 244, 366, 488, . . . . )
 Step 2: The common multiples from the multiples of 14 and 122 are 854, 1708, . . .
 Step 3: The smallest common multiple of 14 and 122 is 854.
∴ The least common multiple of 14 and 122 = 854.
LCM of 14 and 122 by Prime Factorization
Prime factorization of 14 and 122 is (2 × 7) = 2^{1} × 7^{1} and (2 × 61) = 2^{1} × 61^{1} respectively. LCM of 14 and 122 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 7^{1} × 61^{1} = 854.
Hence, the LCM of 14 and 122 by prime factorization is 854.
☛ Also Check:
 LCM of 3, 6, 9 and 12  36
 LCM of 3, 4, 5 and 6  60
 LCM of 28, 36, 45 and 60  1260
 LCM of 24, 36, 44 and 62  24552
 LCM of 21, 28, 36 and 45  1260
 LCM of 2, 4, 6 and 8  24
 LCM of 2, 3, 4 and 5  60
LCM of 14 and 122 Examples

Example 1: Find the smallest number that is divisible by 14 and 122 exactly.
Solution:
The value of LCM(14, 122) will be the smallest number that is exactly divisible by 14 and 122.
⇒ Multiples of 14 and 122: Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, . . . ., 812, 826, 840, 854, . . . .
 Multiples of 122 = 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220, . . . ., 610, 732, 854, . . . .
Therefore, the LCM of 14 and 122 is 854.

Example 2: The product of two numbers is 1708. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 1708
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1708/2
Therefore, the LCM is 854.
The probable combination for the given case is LCM(14, 122) = 854. 
Example 3: Verify the relationship between GCF and LCM of 14 and 122.
Solution:
The relation between GCF and LCM of 14 and 122 is given as,
LCM(14, 122) × GCF(14, 122) = Product of 14, 122
Prime factorization of 14 and 122 is given as, 14 = (2 × 7) = 2^{1} × 7^{1} and 122 = (2 × 61) = 2^{1} × 61^{1}
LCM(14, 122) = 854
GCF(14, 122) = 2
LHS = LCM(14, 122) × GCF(14, 122) = 854 × 2 = 1708
RHS = Product of 14, 122 = 14 × 122 = 1708
⇒ LHS = RHS = 1708
Hence, verified.
FAQs on LCM of 14 and 122
What is the LCM of 14 and 122?
The LCM of 14 and 122 is 854. To find the LCM (least common multiple) of 14 and 122, we need to find the multiples of 14 and 122 (multiples of 14 = 14, 28, 42, 56 . . . . 854; multiples of 122 = 122, 244, 366, 488 . . . . 854) and choose the smallest multiple that is exactly divisible by 14 and 122, i.e., 854.
If the LCM of 122 and 14 is 854, Find its GCF.
LCM(122, 14) × GCF(122, 14) = 122 × 14
Since the LCM of 122 and 14 = 854
⇒ 854 × GCF(122, 14) = 1708
Therefore, the GCF (greatest common factor) = 1708/854 = 2.
What is the Relation Between GCF and LCM of 14, 122?
The following equation can be used to express the relation between GCF and LCM of 14 and 122, i.e. GCF × LCM = 14 × 122.
What are the Methods to Find LCM of 14 and 122?
The commonly used methods to find the LCM of 14 and 122 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
Which of the following is the LCM of 14 and 122? 10, 27, 32, 854
The value of LCM of 14, 122 is the smallest common multiple of 14 and 122. The number satisfying the given condition is 854.