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LCM of 22 and 30

LCM of 22 and 30 is the smallest number among all common multiples of 22 and 30. The first few multiples of 22 and 30 are (22, 44, 66, 88, 110, 132, . . . ) and (30, 60, 90, 120, 150, . . . ) respectively. There are 3 commonly used methods to find LCM of 22 and 30 - by prime factorization, by division method, and by listing multiples.

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

What is the LCM of 22 and 30?

Answer: LCM of 22 and 30 is 330.

Explanation:

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

Methods to Find LCM of 22 and 30

Let's look at the different methods for finding the LCM of 22 and 30.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 22 and 30 by Listing Multiples

To calculate the LCM of 22 and 30 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, . . . ) and 30 (30, 60, 90, 120, 150, . . . . )
Step 2: The common multiples from the multiples of 22 and 30 are 330, 660, . . .
Step 3: The smallest common multiple of 22 and 30 is 330.

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

LCM of 22 and 30 by Division Method

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

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

LCM of 22 and 30 by Prime Factorization

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

☛ Also Check:

LCM of 22 and 30 Examples

Example 1: 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(22, 30) = 330.
Example 2: 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 z.
∵ GCD × LCM = 30 × z
⇒ z = (GCD × LCM)/30
⇒ z = (2 × 330)/30
⇒ z = 22
Therefore, the other number is 22.
Example 3: Verify the relationship between GCF and LCM of 22 and 30.

Solution:

The relation between GCF and LCM of 22 and 30 is given as,
LCM(22, 30) × GCF(22, 30) = Product of 22, 30
Prime factorization of 22 and 30 is given as, 22 = (2 × 11) = 2¹ × 11¹ and 30 = (2 × 3 × 5) = 2¹ × 3¹ × 5¹
LCM(22, 30) = 330
GCF(22, 30) = 2
LHS = LCM(22, 30) × GCF(22, 30) = 330 × 2 = 660
RHS = Product of 22, 30 = 22 × 30 = 660
⇒ LHS = RHS = 660
Hence, verified.

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FAQs on LCM of 22 and 30

What is the LCM of 22 and 30?

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

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

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

Which of the following is the LCM of 22 and 30? 330, 16, 3, 24

The value of LCM of 22, 30 is the smallest common multiple of 22 and 30. The number satisfying the given condition is 330.

What is the Least Perfect Square Divisible by 22 and 30?

The least number divisible by 22 and 30 = LCM(22, 30)
LCM of 22 and 30 = 2 × 3 × 5 × 11 [Incomplete pair(s): 2, 3, 5, 11]
⇒ Least perfect square divisible by each 22 and 30 = LCM(22, 30) × 2 × 3 × 5 × 11 = 108900 [Square root of 108900 = √108900 = ±330]
Therefore, 108900 is the required number.

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

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

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