LCM the 22 and also 30 is the the smallest number amongst all common multiples the 22 and also 30. The first couple of multiples the 22 and also 30 are (22, 44, 66, 88, 110, 132, . . . ) and also (30, 60, 90, 120, 150, . . . ) respectively. There room 3 typically used approaches to find LCM of 22 and also 30 - by element factorization, by department method, and also by listing multiples.

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

Answer: LCM the 22 and also 30 is 330.

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Explanation:

The LCM of 2 non-zero integers, x(22) and also y(30), is the smallest hopeful integer m(330) that is divisible through both x(22) and y(30) without any type of remainder.


Let's look in ~ the different methods because that finding the LCM that 22 and also 30.

By Listing MultiplesBy department MethodBy prime Factorization Method

LCM the 22 and also 30 through Listing Multiples

To calculation the LCM that 22 and also 30 by listing the end the usual multiples, we have the right to follow the given below steps:

Step 1: list a couple of multiples the 22 (22, 44, 66, 88, 110, 132, . . . ) and also 30 (30, 60, 90, 120, 150, . . . . )Step 2: The usual multiples from the multiples that 22 and also 30 are 330, 660, . . .Step 3: The smallest typical multiple that 22 and also 30 is 330.

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

LCM the 22 and 30 by department Method

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To calculation the LCM the 22 and 30 through the department method, we will divide the numbers(22, 30) by their prime determinants (preferably common). The product of this divisors gives the LCM that 22 and 30.

Step 3: continue the actions until only 1s are left in the critical row.

The LCM of 22 and 30 is the product of all prime numbers on the left, i.e. LCM(22, 30) by department method = 2 × 3 × 5 × 11 = 330.

LCM of 22 and also 30 by prime Factorization

Prime administer of 22 and also 30 is (2 × 11) = 21 × 111 and also (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM of 22 and also 30 have the right to be derived by multiplying prime determinants raised to your respective highest possible power, i.e. 21 × 31 × 51 × 111 = 330.Hence, the LCM that 22 and also 30 by prime factorization is 330.

☛ additionally Check:


Example 3: Verify the relationship between GCF and also LCM that 22 and also 30.

Solution:

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


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FAQs ~ above LCM of 22 and 30

What is the LCM of 22 and 30?

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

What is the Relation between GCF and also LCM that 22, 30?

The following equation can be provided to to express the relation in between GCF and also LCM that 22 and 30, i.e. GCF × LCM = 22 × 30.

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

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

What is the the very least Perfect Square Divisible through 22 and 30?

The least number divisible by 22 and also 30 = LCM(22, 30)LCM the 22 and also 30 = 2 × 3 × 5 × 11 ⇒ the very least perfect square divisible by each 22 and also 30 = LCM(22, 30) × 2 × 3 × 5 × 11 = 108900 Therefore, 108900 is the forced number.

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

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