LCM of 14 and 26
LCM of 14 and 26 is the smallest number among all common multiples of 14 and 26. The first few multiples of 14 and 26 are (14, 28, 42, 56, 70, 84, . . . ) and (26, 52, 78, 104, 130, 156, 182, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 26  by division method, by listing multiples, and by prime factorization.
1.  LCM of 14 and 26 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 26?
Answer: LCM of 14 and 26 is 182.
Explanation:
The LCM of two nonzero integers, x(14) and y(26), is the smallest positive integer m(182) that is divisible by both x(14) and y(26) without any remainder.
Methods to Find LCM of 14 and 26
The methods to find the LCM of 14 and 26 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 14 and 26 by Prime Factorization
Prime factorization of 14 and 26 is (2 × 7) = 2^{1} × 7^{1} and (2 × 13) = 2^{1} × 13^{1} respectively. LCM of 14 and 26 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 7^{1} × 13^{1} = 182.
Hence, the LCM of 14 and 26 by prime factorization is 182.
LCM of 14 and 26 by Listing Multiples
To calculate the LCM of 14 and 26 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 26 (26, 52, 78, 104, 130, 156, 182, . . . . )
 Step 2: The common multiples from the multiples of 14 and 26 are 182, 364, . . .
 Step 3: The smallest common multiple of 14 and 26 is 182.
∴ The least common multiple of 14 and 26 = 182.
LCM of 14 and 26 by Division Method
To calculate the LCM of 14 and 26 by the division method, we will divide the numbers(14, 26) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 26.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 26. Write this prime number(2) on the left of the given numbers(14 and 26), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 26) 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 26 is the product of all prime numbers on the left, i.e. LCM(14, 26) by division method = 2 × 7 × 13 = 182.
☛ Also Check:
 LCM of 75 and 69  1725
 LCM of 75 and 105  525
 LCM of 75 and 100  300
 LCM of 72 and 96  288
 LCM of 72 and 84  504
 LCM of 72 and 24  72
 LCM of 72 and 120  360
LCM of 14 and 26 Examples

Example 1: The GCD and LCM of two numbers are 2 and 182 respectively. If one number is 26, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 26 × b
⇒ b = (GCD × LCM)/26
⇒ b = (2 × 182)/26
⇒ b = 14
Therefore, the other number is 14. 
Example 2: The product of two numbers is 364. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 364
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 364/2
Therefore, the LCM is 182.
The probable combination for the given case is LCM(14, 26) = 182. 
Example 3: Verify the relationship between GCF and LCM of 14 and 26.
Solution:
The relation between GCF and LCM of 14 and 26 is given as,
LCM(14, 26) × GCF(14, 26) = Product of 14, 26
Prime factorization of 14 and 26 is given as, 14 = (2 × 7) = 2^{1} × 7^{1} and 26 = (2 × 13) = 2^{1} × 13^{1}
LCM(14, 26) = 182
GCF(14, 26) = 2
LHS = LCM(14, 26) × GCF(14, 26) = 182 × 2 = 364
RHS = Product of 14, 26 = 14 × 26 = 364
⇒ LHS = RHS = 364
Hence, verified.
FAQs on LCM of 14 and 26
What is the LCM of 14 and 26?
The LCM of 14 and 26 is 182. To find the LCM (least common multiple) of 14 and 26, we need to find the multiples of 14 and 26 (multiples of 14 = 14, 28, 42, 56 . . . . 182; multiples of 26 = 26, 52, 78, 104 . . . . 182) and choose the smallest multiple that is exactly divisible by 14 and 26, i.e., 182.
If the LCM of 26 and 14 is 182, Find its GCF.
LCM(26, 14) × GCF(26, 14) = 26 × 14
Since the LCM of 26 and 14 = 182
⇒ 182 × GCF(26, 14) = 364
Therefore, the GCF (greatest common factor) = 364/182 = 2.
What is the Least Perfect Square Divisible by 14 and 26?
The least number divisible by 14 and 26 = LCM(14, 26)
LCM of 14 and 26 = 2 × 7 × 13 [Incomplete pair(s): 2, 7, 13]
⇒ Least perfect square divisible by each 14 and 26 = LCM(14, 26) × 2 × 7 × 13 = 33124 [Square root of 33124 = √33124 = ±182]
Therefore, 33124 is the required number.
What are the Methods to Find LCM of 14 and 26?
The commonly used methods to find the LCM of 14 and 26 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
How to Find the LCM of 14 and 26 by Prime Factorization?
To find the LCM of 14 and 26 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (26 = 2 × 13). LCM of 14 and 26 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 26.
⇒ LCM of 14, 26 = 2^{1} × 7^{1} × 13^{1} = 182.
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