LCM of 14 and 28
LCM of 14 and 28 is the smallest number among all common multiples of 14 and 28. The first few multiples of 14 and 28 are (14, 28, 42, 56, 70, 84, . . . ) and (28, 56, 84, 112, 140, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 28  by prime factorization, by listing multiples, and by division method.
1.  LCM of 14 and 28 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 28?
Answer: LCM of 14 and 28 is 28.
Explanation:
The LCM of two nonzero integers, x(14) and y(28), is the smallest positive integer m(28) that is divisible by both x(14) and y(28) without any remainder.
Methods to Find LCM of 14 and 28
Let's look at the different methods for finding the LCM of 14 and 28.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 14 and 28 by Division Method
To calculate the LCM of 14 and 28 by the division method, we will divide the numbers(14, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 28.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 28. Write this prime number(2) on the left of the given numbers(14 and 28), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 28) 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 28 is the product of all prime numbers on the left, i.e. LCM(14, 28) by division method = 2 × 2 × 7 = 28.
LCM of 14 and 28 by Prime Factorization
Prime factorization of 14 and 28 is (2 × 7) = 2^{1} × 7^{1} and (2 × 2 × 7) = 2^{2} × 7^{1} respectively. LCM of 14 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 7^{1} = 28.
Hence, the LCM of 14 and 28 by prime factorization is 28.
LCM of 14 and 28 by Listing Multiples
To calculate the LCM of 14 and 28 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, . . . ) and 28 (28, 56, 84, 112, 140, 168, . . . . )
 Step 2: The common multiples from the multiples of 14 and 28 are 28, 56, . . .
 Step 3: The smallest common multiple of 14 and 28 is 28.
∴ The least common multiple of 14 and 28 = 28.
☛ Also Check:
 LCM of 72 and 108  216
 LCM of 70 and 90  630
 LCM of 7 and 9  63
 LCM of 7 and 8  56
 LCM of 7 and 7  7
 LCM of 7 and 56  56
 LCM of 7 and 49  49
LCM of 14 and 28 Examples

Example 1: Verify the relationship between GCF and LCM of 14 and 28.
Solution:
The relation between GCF and LCM of 14 and 28 is given as,
LCM(14, 28) × GCF(14, 28) = Product of 14, 28
Prime factorization of 14 and 28 is given as, 14 = (2 × 7) = 2^{1} × 7^{1} and 28 = (2 × 2 × 7) = 2^{2} × 7^{1}
LCM(14, 28) = 28
GCF(14, 28) = 14
LHS = LCM(14, 28) × GCF(14, 28) = 28 × 14 = 392
RHS = Product of 14, 28 = 14 × 28 = 392
⇒ LHS = RHS = 392
Hence, verified. 
Example 2: Find the smallest number that is divisible by 14 and 28 exactly.
Solution:
The smallest number that is divisible by 14 and 28 exactly is their LCM.
⇒ Multiples of 14 and 28: Multiples of 14 = 14, 28, 42, 56, 70, 84, . . . .
 Multiples of 28 = 28, 56, 84, 112, 140, 168, . . . .
Therefore, the LCM of 14 and 28 is 28.

Example 3: The product of two numbers is 392. If their GCD is 14, what is their LCM?
Solution:
Given: GCD = 14
product of numbers = 392
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 392/14
Therefore, the LCM is 28.
The probable combination for the given case is LCM(14, 28) = 28.
FAQs on LCM of 14 and 28
What is the LCM of 14 and 28?
The LCM of 14 and 28 is 28. To find the least common multiple of 14 and 28, we need to find the multiples of 14 and 28 (multiples of 14 = 14, 28, 42, 56; multiples of 28 = 28, 56, 84, 112) and choose the smallest multiple that is exactly divisible by 14 and 28, i.e., 28.
What is the Least Perfect Square Divisible by 14 and 28?
The least number divisible by 14 and 28 = LCM(14, 28)
LCM of 14 and 28 = 2 × 2 × 7 [Incomplete pair(s): 7]
⇒ Least perfect square divisible by each 14 and 28 = LCM(14, 28) × 7 = 196 [Square root of 196 = √196 = ±14]
Therefore, 196 is the required number.
What is the Relation Between GCF and LCM of 14, 28?
The following equation can be used to express the relation between GCF and LCM of 14 and 28, i.e. GCF × LCM = 14 × 28.
Which of the following is the LCM of 14 and 28? 42, 28, 35, 45
The value of LCM of 14, 28 is the smallest common multiple of 14 and 28. The number satisfying the given condition is 28.
If the LCM of 28 and 14 is 28, Find its GCF.
LCM(28, 14) × GCF(28, 14) = 28 × 14
Since the LCM of 28 and 14 = 28
⇒ 28 × GCF(28, 14) = 392
Therefore, the GCF = 392/28 = 14.