LCM the 30 and also 42 is the the smallest number among all typical multiples that 30 and 42. The first couple of multiples of 30 and also 42 are (30, 60, 90, 120, . . . ) and (42, 84, 126, 168, 210, 252, 294, . . . ) respectively. There space 3 typically used approaches to discover LCM of 30 and also 42 - by division method, by element factorization, and also by listing multiples.

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1.LCM that 30 and also 42
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 30 and 42 is 210.

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Explanation:

The LCM of two non-zero integers, x(30) and y(42), is the smallest optimistic integer m(210) the is divisible through both x(30) and also y(42) without any kind of remainder.


The approaches to find the LCM the 30 and also 42 are described below.

By element Factorization MethodBy division MethodBy Listing Multiples

LCM of 30 and also 42 by prime Factorization

Prime factorization of 30 and 42 is (2 × 3 × 5) = 21 × 31 × 51 and also (2 × 3 × 7) = 21 × 31 × 71 respectively. LCM that 30 and also 42 have the right to be obtained by multiplying prime factors raised to their respective highest possible power, i.e. 21 × 31 × 51 × 71 = 210.Hence, the LCM that 30 and also 42 by element factorization is 210.

LCM of 30 and also 42 by division Method

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To calculation the LCM that 30 and also 42 by the department method, we will divide the numbers(30, 42) by your prime components (preferably common). The product of this divisors offers the LCM of 30 and 42.

Step 3: proceed the steps until just 1s are left in the critical row.

The LCM of 30 and also 42 is the product of all prime number on the left, i.e. LCM(30, 42) by division method = 2 × 3 × 5 × 7 = 210.

LCM the 30 and 42 by Listing Multiples

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To calculation the LCM the 30 and 42 through listing the end the typical multiples, we deserve to follow the given below steps:

Step 1: list a couple of multiples of 30 (30, 60, 90, 120, . . . ) and also 42 (42, 84, 126, 168, 210, 252, 294, . . . . )Step 2: The usual multiples indigenous the multiples of 30 and also 42 space 210, 420, . . .Step 3: The smallest common multiple that 30 and 42 is 210.

∴ The least typical multiple the 30 and 42 = 210.

☛ likewise Check:


Example 3: Verify the relationship in between GCF and LCM that 30 and also 42.

Solution:

The relation in between GCF and also LCM the 30 and 42 is given as,LCM(30, 42) × GCF(30, 42) = Product the 30, 42Prime administrate of 30 and also 42 is offered as, 30 = (2 × 3 × 5) = 21 × 31 × 51 and also 42 = (2 × 3 × 7) = 21 × 31 × 71LCM(30, 42) = 210GCF(30, 42) = 6LHS = LCM(30, 42) × GCF(30, 42) = 210 × 6 = 1260RHS = Product of 30, 42 = 30 × 42 = 1260⇒ LHS = RHS = 1260Hence, verified.


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FAQs ~ above LCM that 30 and 42

What is the LCM that 30 and 42?

The LCM of 30 and 42 is 210. To find the LCM (least usual multiple) the 30 and 42, we require to find the multiples of 30 and 42 (multiples the 30 = 30, 60, 90, 120 . . . . 210; multiples the 42 = 42, 84, 126, 168 . . . . 210) and choose the smallest multiple the is specifically divisible by 30 and 42, i.e., 210.

If the LCM that 42 and 30 is 210, discover its GCF.

LCM(42, 30) × GCF(42, 30) = 42 × 30Since the LCM the 42 and 30 = 210⇒ 210 × GCF(42, 30) = 1260Therefore, the greatest typical factor (GCF) = 1260/210 = 6.

What space the approaches to uncover LCM of 30 and also 42?

The frequently used methods to uncover the LCM that 30 and also 42 are:

Prime administrate MethodDivision MethodListing Multiples

What is the Relation in between GCF and also LCM that 30, 42?

The complying with equation can be provided to express the relation between GCF and also LCM of 30 and also 42, i.e. GCF × LCM = 30 × 42.

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How to discover the LCM of 30 and 42 by prime Factorization?

To discover the LCM the 30 and 42 using prime factorization, we will discover the element factors, (30 = 2 × 3 × 5) and also (42 = 2 × 3 × 7). LCM of 30 and 42 is the product the prime components raised to your respective highest exponent amongst the numbers 30 and 42.⇒ LCM the 30, 42 = 21 × 31 × 51 × 71 = 210.