LCM of 14 and 21
LCM of 14 and 21 is the smallest number among all common multiples of 14 and 21. The first few multiples of 14 and 21 are (14, 28, 42, 56, . . . ) and (21, 42, 63, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 21  by listing multiples, by prime factorization, and by division method.
1.  LCM of 14 and 21 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 21?
Answer: LCM of 14 and 21 is 42.
Explanation:
The LCM of two nonzero integers, x(14) and y(21), is the smallest positive integer m(42) that is divisible by both x(14) and y(21) without any remainder.
Methods to Find LCM of 14 and 21
Let's look at the different methods for finding the LCM of 14 and 21.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 14 and 21 by Prime Factorization
Prime factorization of 14 and 21 is (2 × 7) = 2^{1} × 7^{1} and (3 × 7) = 3^{1} × 7^{1} respectively. LCM of 14 and 21 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 14 and 21 by prime factorization is 42.
LCM of 14 and 21 by Listing Multiples
To calculate the LCM of 14 and 21 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, . . . ) and 21 (21, 42, 63, 84, . . . . )
 Step 2: The common multiples from the multiples of 14 and 21 are 42, 84, . . .
 Step 3: The smallest common multiple of 14 and 21 is 42.
∴ The least common multiple of 14 and 21 = 42.
LCM of 14 and 21 by Division Method
To calculate the LCM of 14 and 21 by the division method, we will divide the numbers(14, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 21.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 21. Write this prime number(2) on the left of the given numbers(14 and 21), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 21) 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 21 is the product of all prime numbers on the left, i.e. LCM(14, 21) by division method = 2 × 3 × 7 = 42.
☛ Also Check:
 LCM of 80 and 120  240
 LCM of 8 and 9  72
 LCM of 8 and 64  64
 LCM of 8 and 56  56
 LCM of 8 and 42  168
 LCM of 8 and 36  72
 LCM of 8 and 32  32
LCM of 14 and 21 Examples

Example 1: The GCD and LCM of two numbers are 7 and 42 respectively. If one number is 21, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 21 × m
⇒ m = (GCD × LCM)/21
⇒ m = (7 × 42)/21
⇒ m = 14
Therefore, the other number is 14. 
Example 2: Find the smallest number that is divisible by 14 and 21 exactly.
Solution:
The smallest number that is divisible by 14 and 21 exactly is their LCM.
⇒ Multiples of 14 and 21: Multiples of 14 = 14, 28, 42, 56, 70, . . . .
 Multiples of 21 = 21, 42, 63, 84, 105, . . . .
Therefore, the LCM of 14 and 21 is 42.

Example 3: The product of two numbers is 294. If their GCD is 7, what is their LCM?
Solution:
Given: GCD = 7
product of numbers = 294
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 294/7
Therefore, the LCM is 42.
The probable combination for the given case is LCM(14, 21) = 42.
FAQs on LCM of 14 and 21
What is the LCM of 14 and 21?
The LCM of 14 and 21 is 42. To find the least common multiple (LCM) of 14 and 21, we need to find the multiples of 14 and 21 (multiples of 14 = 14, 28, 42, 56; multiples of 21 = 21, 42, 63, 84) and choose the smallest multiple that is exactly divisible by 14 and 21, i.e., 42.
Which of the following is the LCM of 14 and 21? 11, 3, 12, 42
The value of LCM of 14, 21 is the smallest common multiple of 14 and 21. The number satisfying the given condition is 42.
How to Find the LCM of 14 and 21 by Prime Factorization?
To find the LCM of 14 and 21 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (21 = 3 × 7). LCM of 14 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 21.
⇒ LCM of 14, 21 = 2^{1} × 3^{1} × 7^{1} = 42.
What is the Least Perfect Square Divisible by 14 and 21?
The least number divisible by 14 and 21 = LCM(14, 21)
LCM of 14 and 21 = 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 14 and 21 = LCM(14, 21) × 2 × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.
If the LCM of 21 and 14 is 42, Find its GCF.
LCM(21, 14) × GCF(21, 14) = 21 × 14
Since the LCM of 21 and 14 = 42
⇒ 42 × GCF(21, 14) = 294
Therefore, the GCF = 294/42 = 7.
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