LCM of 5, 6, and also 7 is the smallest number among all usual multiples of 5, 6, and 7. The first few multiples of 5, 6, and 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 find LCM the 5, 6, 7 - through listing multiples, by division method, and by element factorization.

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

Answer: LCM that 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 optimistic integer m(210) that is divisible by a(5), b(6), and c(7) without any remainder.

The techniques to uncover the LCM of 5, 6, and also 7 are described below.

By element Factorization MethodBy division MethodBy Listing Multiples

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

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

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

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

Step 2: If any of the given numbers (5, 6, 7) is a lot of of 2, divide it by 2 and write the quotient listed below it. Bring down any number that is not divisible by the element number.Step 3: continue the measures until only 1s room left in the critical row.

The LCM the 5, 6, and 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 the 5, 6, 7 through listing out the usual multiples, we have the right to follow the given below steps:

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

∴ The least common multiple the 5, 6, and 7 = 210.

☛ also Check:

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

Solution:

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

Multiples that 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 of 5, 6, and also 7 is 210.

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

Solution:

The relation in between GCD and LCM the 5, 6, and 7 is given as,LCM(5, 6, 7) = <(5 × 6 × 7) × GCD(5, 6, 7)>/⇒ element factorization the 5, 6 and also 7:

5 = 516 = 21 × 317 = 71

∴ GCD that (5, 6), (6, 7), (5, 7) and also (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: calculation the LCM of 5, 6, and also 7 making use of the GCD the the provided 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 ~ above LCM of 5, 6, and also 7

### What is the LCM that 5, 6, and 7?

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

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

The adhering to equation have the right to be provided to 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 least Perfect Square Divisible by 5, 6, and also 7?

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

### What room the methods to uncover LCM the 5, 6, 7?

The commonly used methods to uncover the LCM of 5, 6, 7 are: