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.

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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

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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

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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.

☛ additionally Check:


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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FAQs ~ above LCM of 2, 3, and also 7

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:

Prime administer MethodDivision MethodListing Multiples

What is the least Perfect Square Divisible through 2, 3, and 7?

The the very least number divisible by 2, 3, and 7 = LCM(2, 3, 7)LCM that 2, 3, and also 7 = 2 × 3 × 7 ⇒ the very least perfect square divisible by each 2, 3, and also 7 = LCM(2, 3, 7) × 2 × 3 × 7 = 1764 Therefore, 1764 is the forced number.

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What is the Relation in between GCF and also LCM that 2, 3, 7?

The adhering to equation can be offered to express the relation between GCF and LCM the 2, 3, 7, i.e. LCM(2, 3, 7) = <(2 × 3 × 7) × GCF(2, 3, 7)>/.