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LCM of 30 and 22

LCM of 30 and 22 is the smallest number among all common multiples of 30 and 22. The first few multiples of 30 and 22 are (30, 60, 90, 120, 150, 180, 210, . . . ) and (22, 44, 66, 88, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 22 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 30 and 22
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 30 and 22?

Answer: LCM of 30 and 22 is 330.

Explanation:

The LCM of two non-zero integers, x(30) and y(22), is the smallest positive integer m(330) that is divisible by both x(30) and y(22) without any remainder.

Methods to Find LCM of 30 and 22

The methods to find the LCM of 30 and 22 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 30 and 22 by Listing Multiples

To calculate the LCM of 30 and 22 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 30 (30, 60, 90, 120, 150, 180, 210, . . . ) and 22 (22, 44, 66, 88, . . . . )
Step 2: The common multiples from the multiples of 30 and 22 are 330, 660, . . .
Step 3: The smallest common multiple of 30 and 22 is 330.

∴ The least common multiple of 30 and 22 = 330.

LCM of 30 and 22 by Division Method

To calculate the LCM of 30 and 22 by the division method, we will divide the numbers(30, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 22.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 22. Write this prime number(2) on the left of the given numbers(30 and 22), separated as per the ladder arrangement.
Step 2: If any of the given numbers (30, 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 30 and 22 is the product of all prime numbers on the left, i.e. LCM(30, 22) by division method = 2 × 3 × 5 × 11 = 330.

LCM of 30 and 22 by Prime Factorization

Prime factorization of 30 and 22 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (2 × 11) = 2¹ × 11¹ respectively. LCM of 30 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ × 11¹ = 330.
Hence, the LCM of 30 and 22 by prime factorization is 330.

☛ Also Check:

LCM of 30 and 22 Examples

Example 1: The GCD and LCM of two numbers are 2 and 330 respectively. If one number is 30, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 30 × a
⇒ a = (GCD × LCM)/30
⇒ a = (2 × 330)/30
⇒ a = 22
Therefore, the other number is 22.
Example 2: Verify the relationship between GCF and LCM of 30 and 22.

Solution:

The relation between GCF and LCM of 30 and 22 is given as,
LCM(30, 22) × GCF(30, 22) = Product of 30, 22
Prime factorization of 30 and 22 is given as, 30 = (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and 22 = (2 × 11) = 2¹ × 11¹
LCM(30, 22) = 330
GCF(30, 22) = 2
LHS = LCM(30, 22) × GCF(30, 22) = 330 × 2 = 660
RHS = Product of 30, 22 = 30 × 22 = 660
⇒ LHS = RHS = 660
Hence, verified.
Example 3: The product of two numbers is 660. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 660
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 660/2
Therefore, the LCM is 330.
The probable combination for the given case is LCM(30, 22) = 330.

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FAQs on LCM of 30 and 22

What is the LCM of 30 and 22?

The LCM of 30 and 22 is 330. To find the LCM of 30 and 22, we need to find the multiples of 30 and 22 (multiples of 30 = 30, 60, 90, 120 . . . . 330; multiples of 22 = 22, 44, 66, 88 . . . . 330) and choose the smallest multiple that is exactly divisible by 30 and 22, i.e., 330.

If the LCM of 22 and 30 is 330, Find its GCF.

LCM(22, 30) × GCF(22, 30) = 22 × 30
Since the LCM of 22 and 30 = 330
⇒ 330 × GCF(22, 30) = 660
Therefore, the greatest common factor = 660/330 = 2.

How to Find the LCM of 30 and 22 by Prime Factorization?

To find the LCM of 30 and 22 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (22 = 2 × 11). LCM of 30 and 22 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 22.
⇒ LCM of 30, 22 = 2¹ × 3¹ × 5¹ × 11¹ = 330.

What is the Relation Between GCF and LCM of 30, 22?

The following equation can be used to express the relation between GCF and LCM of 30 and 22, i.e. GCF × LCM = 30 × 22.

What are the Methods to Find LCM of 30 and 22?

The commonly used methods to find the LCM of 30 and 22 are:

Division Method
Listing Multiples
Prime Factorization Method

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