LCM of 5, 6, and 7 is the the smallest number amongst all common multiples of 5, 6, and 7. The first couple of multiples that 5, 6, and 7 are (5, 10, 15, 20, 25 . . .), (6, 12, 18, 24, 30 . . .), and (7, 14, 21, 28, 35 . . .) respectively. There room 3 commonly used methods to discover LCM of 5, 6, 7 - by listing multiples, by division method, and by element factorization.

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

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

The LCM of 3 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 type of remainder.

The methods to uncover the LCM the 5, 6, and also 7 are explained below.

By prime Factorization MethodBy division MethodBy Listing Multiples

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

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

### LCM of 5, 6, and also 7 by division Method To calculation the LCM the 5, 6, and also 7 through the division method, we will divide the numbers(5, 6, 7) by your prime factors (preferably common). The product of these divisors provides the LCM of 5, 6, and 7.

Step 2: If any type of of the given numbers (5, 6, 7) is a many of 2, division it by 2 and write the quotient listed below it. Bring down any kind of number that is no divisible by the prime number.Step 3: continue the measures until only 1s space left in the last row.

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

### LCM the 5, 6, and also 7 by Listing Multiples To calculate the LCM that 5, 6, 7 by listing out the usual multiples, we deserve to follow the given listed below steps:

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

∴ The least usual multiple that 5, 6, and 7 = 210.

☛ also Check:

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

Solution:

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

Multiples the 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 200, 205, 210, . . . .Multiples the 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 that 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 in between GCD and also LCM that 5, 6, and 7 is offered as,LCM(5, 6, 7) = <(5 × 6 × 7) × GCD(5, 6, 7)>/⇒ prime factorization the 5, 6 and also 7:

5 = 516 = 21 × 317 = 71

∴ GCD of (5, 6), (6, 7), (5, 7) and also (5, 6, 7) = 1, 1, 1 and also 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 the 5, 6, and also 7 utilizing the GCD the 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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### What is the LCM that 5, 6, and also 7?

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

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

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

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

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

### What space the techniques to find LCM that 5, 6, 7?

The frequently used methods to find the LCM that 5, 6, 7 are: