LCM of 12 and 22
LCM of 12 and 22 is the smallest number among all common multiples of 12 and 22. The first few multiples of 12 and 22 are (12, 24, 36, 48, 60, . . . ) and (22, 44, 66, 88, 110, 132, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 22  by listing multiples, by prime factorization, and by division method.
1.  LCM of 12 and 22 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 12 and 22?
Answer: LCM of 12 and 22 is 132.
Explanation:
The LCM of two nonzero integers, x(12) and y(22), is the smallest positive integer m(132) that is divisible by both x(12) and y(22) without any remainder.
Methods to Find LCM of 12 and 22
The methods to find the LCM of 12 and 22 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 12 and 22 by Division Method
To calculate the LCM of 12 and 22 by the division method, we will divide the numbers(12, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 22.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 22. Write this prime number(2) on the left of the given numbers(12 and 22), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (12, 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 12 and 22 is the product of all prime numbers on the left, i.e. LCM(12, 22) by division method = 2 × 2 × 3 × 11 = 132.
LCM of 12 and 22 by Prime Factorization
Prime factorization of 12 and 22 is (2 × 2 × 3) = 2^{2} × 3^{1} and (2 × 11) = 2^{1} × 11^{1} respectively. LCM of 12 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 11^{1} = 132.
Hence, the LCM of 12 and 22 by prime factorization is 132.
LCM of 12 and 22 by Listing Multiples
To calculate the LCM of 12 and 22 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, . . . ) and 22 (22, 44, 66, 88, 110, 132, . . . . )
 Step 2: The common multiples from the multiples of 12 and 22 are 132, 264, . . .
 Step 3: The smallest common multiple of 12 and 22 is 132.
∴ The least common multiple of 12 and 22 = 132.
☛ Also Check:
 LCM of 13 and 20  260
 LCM of 13 and 17  221
 LCM of 13 and 16  208
 LCM of 13 and 15  195
 LCM of 13 and 14  182
 LCM of 13 and 11  143
 LCM of 125 and 75  375
LCM of 12 and 22 Examples

Example 1: Verify the relationship between GCF and LCM of 12 and 22.
Solution:
The relation between GCF and LCM of 12 and 22 is given as,
LCM(12, 22) × GCF(12, 22) = Product of 12, 22
Prime factorization of 12 and 22 is given as, 12 = (2 × 2 × 3) = 2^{2} × 3^{1} and 22 = (2 × 11) = 2^{1} × 11^{1}
LCM(12, 22) = 132
GCF(12, 22) = 2
LHS = LCM(12, 22) × GCF(12, 22) = 132 × 2 = 264
RHS = Product of 12, 22 = 12 × 22 = 264
⇒ LHS = RHS = 264
Hence, verified. 
Example 2: Find the smallest number that is divisible by 12 and 22 exactly.
Solution:
The smallest number that is divisible by 12 and 22 exactly is their LCM.
⇒ Multiples of 12 and 22: Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, . . . .
 Multiples of 22 = 22, 44, 66, 88, 110, 132, . . . .
Therefore, the LCM of 12 and 22 is 132.

Example 3: The product of two numbers is 264. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 264
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 264/2
Therefore, the LCM is 132.
The probable combination for the given case is LCM(12, 22) = 132.
FAQs on LCM of 12 and 22
What is the LCM of 12 and 22?
The LCM of 12 and 22 is 132. To find the LCM (least common multiple) of 12 and 22, we need to find the multiples of 12 and 22 (multiples of 12 = 12, 24, 36, 48 . . . . 132; multiples of 22 = 22, 44, 66, 88 . . . . 132) and choose the smallest multiple that is exactly divisible by 12 and 22, i.e., 132.
What is the Relation Between GCF and LCM of 12, 22?
The following equation can be used to express the relation between GCF and LCM of 12 and 22, i.e. GCF × LCM = 12 × 22.
How to Find the LCM of 12 and 22 by Prime Factorization?
To find the LCM of 12 and 22 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (22 = 2 × 11). LCM of 12 and 22 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 22.
⇒ LCM of 12, 22 = 2^{2} × 3^{1} × 11^{1} = 132.
If the LCM of 22 and 12 is 132, Find its GCF.
LCM(22, 12) × GCF(22, 12) = 22 × 12
Since the LCM of 22 and 12 = 132
⇒ 132 × GCF(22, 12) = 264
Therefore, the greatest common factor = 264/132 = 2.
What are the Methods to Find LCM of 12 and 22?
The commonly used methods to find the LCM of 12 and 22 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
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