LCM that 21 and also 30 is the smallest number amongst all common multiples the 21 and 30. The first couple of multiples that 21 and 30 space (21, 42, 63, 84, 105, . . . ) and (30, 60, 90, 120, . . . ) respectively. There space 3 frequently used techniques to find LCM that 21 and 30 - by division method, by listing multiples, and also by prime factorization.

You are watching: What is the least common multiple of 21 and 30

1.LCM the 21 and 30
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 21 and 30 is 210.

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Explanation:

The LCM of 2 non-zero integers, x(21) and also y(30), is the smallest positive integer m(210) that is divisible through both x(21) and also y(30) without any kind of remainder.


The techniques to find the LCM of 21 and 30 are described below.

By division MethodBy element Factorization MethodBy Listing Multiples

LCM that 21 and 30 by division Method

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To calculation the LCM of 21 and 30 through the department method, we will divide the numbers(21, 30) by their prime factors (preferably common). The product of this divisors offers the LCM of 21 and also 30.

Step 3: continue the measures until only 1s room left in the last row.

The LCM that 21 and 30 is the product of every prime numbers on the left, i.e. LCM(21, 30) by department method = 2 × 3 × 5 × 7 = 210.

LCM that 21 and 30 by prime Factorization

Prime administrate of 21 and also 30 is (3 × 7) = 31 × 71 and (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM the 21 and also 30 deserve to be acquired by multiply prime components raised to their respective highest possible power, i.e. 21 × 31 × 51 × 71 = 210.Hence, the LCM of 21 and 30 by element factorization is 210.

LCM the 21 and 30 through Listing Multiples

To calculation the LCM of 21 and also 30 through listing the end the usual multiples, we deserve to follow the given listed below steps:

Step 1: perform a couple of multiples the 21 (21, 42, 63, 84, 105, . . . ) and also 30 (30, 60, 90, 120, . . . . )Step 2: The common multiples indigenous the multiples that 21 and also 30 space 210, 420, . . .Step 3: The smallest common multiple that 21 and also 30 is 210.

∴ The least usual multiple of 21 and 30 = 210.

☛ also Check:


Example 1: Verify the relationship between GCF and LCM that 21 and 30.

Solution:

The relation between GCF and LCM of 21 and 30 is given as,LCM(21, 30) × GCF(21, 30) = Product the 21, 30Prime administer of 21 and also 30 is offered as, 21 = (3 × 7) = 31 × 71 and 30 = (2 × 3 × 5) = 21 × 31 × 51LCM(21, 30) = 210GCF(21, 30) = 3LHS = LCM(21, 30) × GCF(21, 30) = 210 × 3 = 630RHS = Product the 21, 30 = 21 × 30 = 630⇒ LHS = RHS = 630Hence, verified.


Example 2: discover the the smallest number that is divisible through 21 and also 30 exactly.

Solution:

The smallest number that is divisible by 21 and also 30 precisely is your LCM.⇒ Multiples of 21 and 30:

Multiples the 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . .Multiples the 30 = 30, 60, 90, 120, 150, 180, 210, . . . .

Therefore, the LCM the 21 and also 30 is 210.


Example 3: The product of two numbers is 630. If your GCD is 3, what is their LCM?

Solution:

Given: GCD = 3product of number = 630∵ LCM × GCD = product the numbers⇒ LCM = Product/GCD = 630/3Therefore, the LCM is 210.The probable mix for the given case is LCM(21, 30) = 210.


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FAQs ~ above LCM the 21 and also 30

What is the LCM that 21 and 30?

If the LCM that 30 and also 21 is 210, uncover its GCF.

LCM(30, 21) × GCF(30, 21) = 30 × 21Since the LCM the 30 and 21 = 210⇒ 210 × GCF(30, 21) = 630Therefore, the greatest usual factor (GCF) = 630/210 = 3.

Which that the complying with is the LCM the 21 and also 30? 210, 5, 15, 16

The value of LCM that 21, 30 is the smallest usual multiple of 21 and also 30. The number to solve the given condition is 210.

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What are the methods to uncover LCM that 21 and also 30?

The typically used approaches to find the LCM of 21 and also 30 are:

Prime factorization MethodListing MultiplesDivision Method

What is the the very least Perfect Square Divisible by 21 and 30?

The the very least number divisible by 21 and 30 = LCM(21, 30)LCM the 21 and also 30 = 2 × 3 × 5 × 7 ⇒ the very least perfect square divisible by each 21 and 30 = LCM(21, 30) × 2 × 3 × 5 × 7 = 44100 Therefore, 44100 is the forced number.