LCM of 6 and 14
LCM of 6 and 14 is the smallest number among all common multiples of 6 and 14. The first few multiples of 6 and 14 are (6, 12, 18, 24, 30, . . . ) and (14, 28, 42, 56, 70, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 14  by division method, by listing multiples, and by prime factorization.
1.  LCM of 6 and 14 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 6 and 14?
Answer: LCM of 6 and 14 is 42.
Explanation:
The LCM of two nonzero integers, x(6) and y(14), is the smallest positive integer m(42) that is divisible by both x(6) and y(14) without any remainder.
Methods to Find LCM of 6 and 14
The methods to find the LCM of 6 and 14 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 6 and 14 by Division Method
To calculate the LCM of 6 and 14 by the division method, we will divide the numbers(6, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 14.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 14. Write this prime number(2) on the left of the given numbers(6 and 14), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (6, 14) 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 6 and 14 is the product of all prime numbers on the left, i.e. LCM(6, 14) by division method = 2 × 3 × 7 = 42.
LCM of 6 and 14 by Prime Factorization
Prime factorization of 6 and 14 is (2 × 3) = 2^{1} × 3^{1} and (2 × 7) = 2^{1} × 7^{1} respectively. LCM of 6 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 7^{1} = 42.
Hence, the LCM of 6 and 14 by prime factorization is 42.
LCM of 6 and 14 by Listing Multiples
To calculate the LCM of 6 and 14 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, . . . ) and 14 (14, 28, 42, 56, 70, 84, . . . . )
 Step 2: The common multiples from the multiples of 6 and 14 are 42, 84, . . .
 Step 3: The smallest common multiple of 6 and 14 is 42.
∴ The least common multiple of 6 and 14 = 42.
☛ Also Check:
 LCM of 9 and 18  18
 LCM of 2 and 3  6
 LCM of 378, 180 and 420  3780
 LCM of 6, 9 and 15  90
 LCM of 2, 3 and 4  12
 LCM of 2601 and 2616  2268072
 LCM of 4 and 8  8
LCM of 6 and 14 Examples

Example 1: The GCD and LCM of two numbers are 2 and 42 respectively. If one number is 6, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 6 × b
⇒ b = (GCD × LCM)/6
⇒ b = (2 × 42)/6
⇒ b = 14
Therefore, the other number is 14. 
Example 2: Find the smallest number that is divisible by 6 and 14 exactly.
Solution:
The smallest number that is divisible by 6 and 14 exactly is their LCM.
⇒ Multiples of 6 and 14: Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, . . . .
 Multiples of 14 = 14, 28, 42, 56, 70, 84, . . . .
Therefore, the LCM of 6 and 14 is 42.

Example 3: The product of two numbers is 84. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 84
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 84/2
Therefore, the LCM is 42.
The probable combination for the given case is LCM(6, 14) = 42.
FAQs on LCM of 6 and 14
What is the LCM of 6 and 14?
The LCM of 6 and 14 is 42. To find the LCM of 6 and 14, we need to find the multiples of 6 and 14 (multiples of 6 = 6, 12, 18, 24 . . . . 42; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 6 and 14, i.e., 42.
If the LCM of 14 and 6 is 42, Find its GCF.
LCM(14, 6) × GCF(14, 6) = 14 × 6
Since the LCM of 14 and 6 = 42
⇒ 42 × GCF(14, 6) = 84
Therefore, the greatest common factor = 84/42 = 2.
What is the Least Perfect Square Divisible by 6 and 14?
The least number divisible by 6 and 14 = LCM(6, 14)
LCM of 6 and 14 = 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 6 and 14 = LCM(6, 14) × 2 × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.
How to Find the LCM of 6 and 14 by Prime Factorization?
To find the LCM of 6 and 14 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (14 = 2 × 7). LCM of 6 and 14 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 14.
⇒ LCM of 6, 14 = 2^{1} × 3^{1} × 7^{1} = 42.
What are the Methods to Find LCM of 6 and 14?
The commonly used methods to find the LCM of 6 and 14 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
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