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LCM of 22 and 44

LCM of 22 and 44 is the smallest number among all common multiples of 22 and 44. The first few multiples of 22 and 44 are (22, 44, 66, 88, 110, 132, 154, . . . ) and (44, 88, 132, 176, 220, 264, 308, . . . ) respectively. There are 3 commonly used methods to find LCM of 22 and 44 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 22 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 22 and 44?

Answer: LCM of 22 and 44 is 44.

Explanation:

The LCM of two non-zero integers, x(22) and y(44), is the smallest positive integer m(44) that is divisible by both x(22) and y(44) without any remainder.

Methods to Find LCM of 22 and 44

The methods to find the LCM of 22 and 44 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 22 and 44 by Prime Factorization

Prime factorization of 22 and 44 is (2 × 11) = 2¹ × 11¹ and (2 × 2 × 11) = 2² × 11¹ respectively. LCM of 22 and 44 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 11¹ = 44.
Hence, the LCM of 22 and 44 by prime factorization is 44.

LCM of 22 and 44 by Listing Multiples

To calculate the LCM of 22 and 44 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 22 (22, 44, 66, 88, 110, 132, 154, . . . ) and 44 (44, 88, 132, 176, 220, 264, 308, . . . . )
Step 2: The common multiples from the multiples of 22 and 44 are 44, 88, . . .
Step 3: The smallest common multiple of 22 and 44 is 44.

∴ The least common multiple of 22 and 44 = 44.

LCM of 22 and 44 by Division Method

To calculate the LCM of 22 and 44 by the division method, we will divide the numbers(22, 44) by their prime factors (preferably common). The product of these divisors gives the LCM of 22 and 44.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 22 and 44. Write this prime number(2) on the left of the given numbers(22 and 44), separated as per the ladder arrangement.
Step 2: If any of the given numbers (22, 44) 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 22 and 44 is the product of all prime numbers on the left, i.e. LCM(22, 44) by division method = 2 × 2 × 11 = 44.

☛ Also Check:

LCM of 22 and 44 Examples

Example 1: The product of two numbers is 968. If their GCD is 22, what is their LCM?

Solution:

Given: GCD = 22
product of numbers = 968
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 968/22
Therefore, the LCM is 44.
The probable combination for the given case is LCM(22, 44) = 44.
Example 2: Find the smallest number that is divisible by 22 and 44 exactly.

Solution:

The smallest number that is divisible by 22 and 44 exactly is their LCM.
⇒ Multiples of 22 and 44:
- Multiples of 22 = 22, 44, 66, 88, 110, 132, . . . .
- Multiples of 44 = 44, 88, 132, 176, 220, 264, . . . .
Therefore, the LCM of 22 and 44 is 44.
Example 3: Verify the relationship between GCF and LCM of 22 and 44.

Solution:

The relation between GCF and LCM of 22 and 44 is given as,
LCM(22, 44) × GCF(22, 44) = Product of 22, 44
Prime factorization of 22 and 44 is given as, 22 = (2 × 11) = 2¹ × 11¹ and 44 = (2 × 2 × 11) = 2² × 11¹
LCM(22, 44) = 44
GCF(22, 44) = 22
LHS = LCM(22, 44) × GCF(22, 44) = 44 × 22 = 968
RHS = Product of 22, 44 = 22 × 44 = 968
⇒ LHS = RHS = 968
Hence, verified.

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FAQs on LCM of 22 and 44

What is the LCM of 22 and 44?

The LCM of 22 and 44 is 44. To find the least common multiple (LCM) of 22 and 44, we need to find the multiples of 22 and 44 (multiples of 22 = 22, 44, 66, 88; multiples of 44 = 44, 88, 132, 176) and choose the smallest multiple that is exactly divisible by 22 and 44, i.e., 44.

What is the Relation Between GCF and LCM of 22, 44?

The following equation can be used to express the relation between GCF and LCM of 22 and 44, i.e. GCF × LCM = 22 × 44.

What is the Least Perfect Square Divisible by 22 and 44?

The least number divisible by 22 and 44 = LCM(22, 44)
LCM of 22 and 44 = 2 × 2 × 11 [Incomplete pair(s): 11]
⇒ Least perfect square divisible by each 22 and 44 = LCM(22, 44) × 11 = 484 [Square root of 484 = √484 = ±22]
Therefore, 484 is the required number.

What are the Methods to Find LCM of 22 and 44?

The commonly used methods to find the LCM of 22 and 44 are:

Listing Multiples
Prime Factorization Method
Division Method

If the LCM of 44 and 22 is 44, Find its GCF.

LCM(44, 22) × GCF(44, 22) = 44 × 22
Since the LCM of 44 and 22 = 44
⇒ 44 × GCF(44, 22) = 968
Therefore, the greatest common factor = 968/44 = 22.

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