LCM the 5, 6, and also 7 is the smallest number amongst all common multiples that 5, 6, and 7. The first couple of multiples that 5, 6, and also 7 space (5, 10, 15, 20, 25 . . .), (6, 12, 18, 24, 30 . . .), and also (7, 14, 21, 28, 35 . . .) respectively. There are 3 frequently used approaches to uncover LCM of 5, 6, 7 - by listing multiples, by department method, and by prime factorization.

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1.LCM of 5, 6, and also 7
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 5, 6, and 7 is 210.

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Explanation:

The LCM of three non-zero integers, a(5), b(6), and c(7), is the smallest positive integer m(210) that is divisible through a(5), b(6), and also c(7) without any remainder.


The approaches to find the LCM that 5, 6, and 7 are defined below.

By element Factorization MethodBy department MethodBy Listing Multiples

LCM of 5, 6, and also 7 by prime Factorization

Prime administer of 5, 6, and also 7 is (5) = 51, (2 × 3) = 21 × 31, and (7) = 71 respectively. LCM that 5, 6, and also 7 can be obtained by multiply prime components raised to their respective greatest power, i.e. 21 × 31 × 51 × 71 = 210.Hence, the LCM the 5, 6, and also 7 by prime factorization is 210.

LCM the 5, 6, and also 7 by department Method

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To calculate the LCM of 5, 6, and also 7 through the division method, we will divide the numbers(5, 6, 7) by their prime factors (preferably common). The product of this divisors gives the LCM that 5, 6, and also 7.

Step 2: If any kind of of the given numbers (5, 6, 7) is a multiple of 2, division it by 2 and also write the quotient listed below it. Bring down any kind of number that is no divisible by the prime number.Step 3: proceed the procedures until just 1s room left in the critical row.

The LCM of 5, 6, and also 7 is the product of every prime number on the left, i.e. LCM(5, 6, 7) by division method = 2 × 3 × 5 × 7 = 210.

LCM of 5, 6, and also 7 through Listing Multiples

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To calculate the LCM that 5, 6, 7 by listing out the typical multiples, we deserve to follow the given below steps:

Step 1: list a few multiples the 5 (5, 10, 15, 20, 25 . . .), 6 (6, 12, 18, 24, 30 . . .), and 7 (7, 14, 21, 28, 35 . . .).Step 2: The typical multiples from the multiples that 5, 6, and also 7 space 210, 420, . . .Step 3: The smallest usual multiple that 5, 6, and 7 is 210.

∴ The least typical multiple of 5, 6, and also 7 = 210.

☛ additionally Check:


Example 1: discover the the smallest number the is divisible through 5, 6, 7 exactly.

Solution:

The value of LCM(5, 6, 7) will be the smallest number the is precisely divisible by 5, 6, and 7.⇒ Multiples the 5, 6, and also 7:

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 200, 205, 210, . . . .Multiples that 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 192, 198, 204, 210, . . . .Multiples that 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 189, 196, 203, 210, . . . .

Therefore, the LCM the 5, 6, and 7 is 210.


Example 2: Verify the relationship between the GCD and LCM the 5, 6, and also 7.

Solution:

The relation between GCD and LCM of 5, 6, and also 7 is offered as,LCM(5, 6, 7) = <(5 × 6 × 7) × GCD(5, 6, 7)>/⇒ prime factorization of 5, 6 and 7:

5 = 516 = 21 × 317 = 71

∴ GCD that (5, 6), (6, 7), (5, 7) and (5, 6, 7) = 1, 1, 1 and 1 respectively.Now, LHS = LCM(5, 6, 7) = 210.And, RHS = <(5 × 6 × 7) × GCD(5, 6, 7)>/ = <(210) × 1>/<1 × 1 × 1> = 210LHS = RHS = 210.Hence verified.


Example 3: calculate the LCM that 5, 6, and 7 using the GCD that the given numbers.

Solution:

Prime administrate of 5, 6, 7:

5 = 516 = 21 × 317 = 71

Therefore, GCD(5, 6) = 1, GCD(6, 7) = 1, GCD(5, 7) = 1, GCD(5, 6, 7) = 1We know,LCM(5, 6, 7) = <(5 × 6 × 7) × GCD(5, 6, 7)>/LCM(5, 6, 7) = (210 × 1)/(1 × 1 × 1) = 210⇒LCM(5, 6, 7) = 210


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FAQs top top LCM the 5, 6, and also 7

What is the LCM of 5, 6, and 7?

The LCM of 5, 6, and also 7 is 210. To find the LCM the 5, 6, and 7, we require to uncover the multiples that 5, 6, and also 7 (multiples the 5 = 5, 10, 15, 20 . . . . 210 . . . . ; multiples the 6 = 6, 12, 18, 24 . . . . 210 . . . . ; multiples of 7 = 7, 14, 21, 28 . . . . 210 . . . . ) and choose the smallest multiple that is exactly divisible through 5, 6, and also 7, i.e., 210.

What is the Relation between GCF and LCM the 5, 6, 7?

The complying with equation can be used to express the relation between GCF and LCM the 5, 6, 7, i.e. LCM(5, 6, 7) = <(5 × 6 × 7) × GCF(5, 6, 7)>/.

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What is the the very least Perfect Square Divisible through 5, 6, and also 7?

The least number divisible through 5, 6, and 7 = LCM(5, 6, 7)LCM the 5, 6, and 7 = 2 × 3 × 5 × 7 ⇒ the very least perfect square divisible by every 5, 6, and also 7 = LCM(5, 6, 7) × 2 × 3 × 5 × 7 = 44100 Therefore, 44100 is the required number.

What are the approaches to uncover LCM of 5, 6, 7?

The typically used methods to discover the LCM that 5, 6, 7 are: