LCM of 21 and 22
LCM of 21 and 22 is the smallest number among all common multiples of 21 and 22. The first few multiples of 21 and 22 are (21, 42, 63, 84, 105, 126, . . . ) and (22, 44, 66, 88, 110, 132, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 22  by division method, by listing multiples, and by prime factorization.
1.  LCM of 21 and 22 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 21 and 22?
Answer: LCM of 21 and 22 is 462.
Explanation:
The LCM of two nonzero integers, x(21) and y(22), is the smallest positive integer m(462) that is divisible by both x(21) and y(22) without any remainder.
Methods to Find LCM of 21 and 22
Let's look at the different methods for finding the LCM of 21 and 22.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 21 and 22 by Division Method
To calculate the LCM of 21 and 22 by the division method, we will divide the numbers(21, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 22.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 22. Write this prime number(2) on the left of the given numbers(21 and 22), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (21, 22) 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 21 and 22 is the product of all prime numbers on the left, i.e. LCM(21, 22) by division method = 2 × 3 × 7 × 11 = 462.
LCM of 21 and 22 by Listing Multiples
To calculate the LCM of 21 and 22 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 21 (21, 42, 63, 84, 105, 126, . . . ) and 22 (22, 44, 66, 88, 110, 132, . . . . )
 Step 2: The common multiples from the multiples of 21 and 22 are 462, 924, . . .
 Step 3: The smallest common multiple of 21 and 22 is 462.
∴ The least common multiple of 21 and 22 = 462.
LCM of 21 and 22 by Prime Factorization
Prime factorization of 21 and 22 is (3 × 7) = 3^{1} × 7^{1} and (2 × 11) = 2^{1} × 11^{1} respectively. LCM of 21 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 7^{1} × 11^{1} = 462.
Hence, the LCM of 21 and 22 by prime factorization is 462.
☛ Also Check:
 LCM of 15 and 25  75
 LCM of 42 and 63  126
 LCM of 3, 5 and 8  120
 LCM of 8, 16 and 24  48
 LCM of 30 and 60  60
 LCM of 21 and 35  105
 LCM of 20 and 24  120
LCM of 21 and 22 Examples

Example 1: The GCD and LCM of two numbers are 1 and 462 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 = (1 × 462)/21
⇒ m = 22
Therefore, the other number is 22. 
Example 2: Verify the relationship between GCF and LCM of 21 and 22.
Solution:
The relation between GCF and LCM of 21 and 22 is given as,
LCM(21, 22) × GCF(21, 22) = Product of 21, 22
Prime factorization of 21 and 22 is given as, 21 = (3 × 7) = 3^{1} × 7^{1} and 22 = (2 × 11) = 2^{1} × 11^{1}
LCM(21, 22) = 462
GCF(21, 22) = 1
LHS = LCM(21, 22) × GCF(21, 22) = 462 × 1 = 462
RHS = Product of 21, 22 = 21 × 22 = 462
⇒ LHS = RHS = 462
Hence, verified. 
Example 3: The product of two numbers is 462. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 462
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 462/1
Therefore, the LCM is 462.
The probable combination for the given case is LCM(21, 22) = 462.
FAQs on LCM of 21 and 22
What is the LCM of 21 and 22?
The LCM of 21 and 22 is 462. To find the LCM (least common multiple) of 21 and 22, we need to find the multiples of 21 and 22 (multiples of 21 = 21, 42, 63, 84 . . . . 462; multiples of 22 = 22, 44, 66, 88 . . . . 462) and choose the smallest multiple that is exactly divisible by 21 and 22, i.e., 462.
What is the Least Perfect Square Divisible by 21 and 22?
The least number divisible by 21 and 22 = LCM(21, 22)
LCM of 21 and 22 = 2 × 3 × 7 × 11 [Incomplete pair(s): 2, 3, 7, 11]
⇒ Least perfect square divisible by each 21 and 22 = LCM(21, 22) × 2 × 3 × 7 × 11 = 213444 [Square root of 213444 = √213444 = ±462]
Therefore, 213444 is the required number.
Which of the following is the LCM of 21 and 22? 12, 27, 462, 15
The value of LCM of 21, 22 is the smallest common multiple of 21 and 22. The number satisfying the given condition is 462.
How to Find the LCM of 21 and 22 by Prime Factorization?
To find the LCM of 21 and 22 using prime factorization, we will find the prime factors, (21 = 3 × 7) and (22 = 2 × 11). LCM of 21 and 22 is the product of prime factors raised to their respective highest exponent among the numbers 21 and 22.
⇒ LCM of 21, 22 = 2^{1} × 3^{1} × 7^{1} × 11^{1} = 462.
If the LCM of 22 and 21 is 462, Find its GCF.
LCM(22, 21) × GCF(22, 21) = 22 × 21
Since the LCM of 22 and 21 = 462
⇒ 462 × GCF(22, 21) = 462
Therefore, the greatest common factor = 462/462 = 1.
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