LCM that 2, 3, and 7 is the the smallest number amongst all typical multiples that 2, 3, and also 7. The first couple of multiples of 2, 3, and also 7 room (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and (7, 14, 21, 28, 35 . . .) respectively. There room 3 frequently used approaches to find LCM the 2, 3, 7 - by element factorization, by listing multiples, and also by division method.

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 1 LCM that 2, 3, and also 7 2 List of Methods 3 Solved Examples 4 FAQs

Answer: LCM of 2, 3, and 7 is 42. Explanation:

The LCM of three non-zero integers, a(2), b(3), and also c(7), is the smallest confident integer m(42) that is divisible by a(2), b(3), and c(7) without any remainder.

Let's look in ~ the different methods because that finding the LCM that 2, 3, and 7.

By prime Factorization MethodBy Listing MultiplesBy department Method

### LCM of 2, 3, and also 7 by prime Factorization

Prime factorization of 2, 3, and also 7 is (2) = 21, (3) = 31, and (7) = 71 respectively. LCM of 2, 3, and also 7 can be derived by multiplying prime components raised to their respective highest possible power, i.e. 21 × 31 × 71 = 42.Hence, the LCM the 2, 3, and 7 by element factorization is 42.

### LCM the 2, 3, and 7 by Listing Multiples To calculation the LCM that 2, 3, 7 through listing out the typical multiples, we deserve to follow the given listed below steps:

Step 1: perform a couple of multiples the 2 (2, 4, 6, 8, 10 . . .), 3 (3, 6, 9, 12, 15 . . .), and also 7 (7, 14, 21, 28, 35 . . .).Step 2: The typical multiples native the multiples that 2, 3, and also 7 room 42, 84, . . .Step 3: The smallest common multiple of 2, 3, and 7 is 42.

∴ The least common multiple that 2, 3, and also 7 = 42.

### LCM of 2, 3, and 7 by department Method To calculation the LCM of 2, 3, and also 7 by the division method, we will divide the numbers(2, 3, 7) by your prime factors (preferably common). The product of this divisors provides the LCM that 2, 3, and 7.

Step 2: If any kind of of the offered numbers (2, 3, 7) is a multiple of 2, division it through 2 and also write the quotient listed below it. Bring down any type of number the is no divisible through the element number.Step 3: proceed the procedures until only 1s space left in the last row.

The LCM of 2, 3, and also 7 is the product of all prime numbers on the left, i.e. LCM(2, 3, 7) by department method = 2 × 3 × 7 = 42.

Example 2: find the the smallest number that is divisible by 2, 3, 7 exactly.

Solution:

The worth of LCM(2, 3, 7) will be the the smallest number that is exactly divisible by 2, 3, and also 7.⇒ Multiples of 2, 3, and 7:

Multiples that 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, . . . ., 38, 40, 42, . . . .Multiples that 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 30, 33, 36, 39, 42, . . . .Multiples that 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 28, 35, 42, . . . .

Therefore, the LCM of 2, 3, and 7 is 42.

Example 3: Verify the relationship in between the GCD and also LCM the 2, 3, and 7.

Solution:

The relation in between GCD and also LCM that 2, 3, and also 7 is provided as,LCM(2, 3, 7) = <(2 × 3 × 7) × GCD(2, 3, 7)>/⇒ element factorization of 2, 3 and 7:

2 = 213 = 317 = 71

∴ GCD of (2, 3), (3, 7), (2, 7) and (2, 3, 7) = 1, 1, 1 and 1 respectively.Now, LHS = LCM(2, 3, 7) = 42.And, RHS = <(2 × 3 × 7) × GCD(2, 3, 7)>/ = <(42) × 1>/<1 × 1 × 1> = 42LHS = RHS = 42.Hence verified.

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### What is the LCM of 2, 3, and 7?

The LCM of 2, 3, and 7 is 42. To find the LCM (least typical multiple) that 2, 3, and also 7, we require to find the multiples the 2, 3, and 7 (multiples that 2 = 2, 4, 6, 8 . . . . 42 . . . . ; multiples the 3 = 3, 6, 9, 12 . . . . 42 . . . . ; multiples the 7 = 7, 14, 21, 28, 42 . . . .) and choose the the smallest multiple the is specifically divisible through 2, 3, and 7, i.e., 42.

### What space the techniques to find LCM the 2, 3, 7?

The frequently used approaches to uncover the LCM of 2, 3, 7 are: