LCM of 2, 3, and also 7 is the smallest number among all usual multiples of 2, 3, and 7. The first few multiples that 2, 3, and also 7 space (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and also (7, 14, 21, 28, 35 . . .) respectively. There space 3 generally used approaches to discover LCM of 2, 3, 7 - by element factorization, by listing multiples, and by division method.

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

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

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Explanation:

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


Let's look at the various methods because that finding the LCM that 2, 3, and 7.

By element Factorization MethodBy Listing MultiplesBy department Method

LCM that 2, 3, and 7 by prime Factorization

Prime administer of 2, 3, and 7 is (2) = 21, (3) = 31, and (7) = 71 respectively. LCM the 2, 3, and also 7 can be obtained by multiplying prime components raised to your 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 through Listing Multiples

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To calculate the LCM that 2, 3, 7 by listing out the typical multiples, we deserve to follow the given below steps:

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

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

LCM of 2, 3, and also 7 by department Method

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To calculate the LCM of 2, 3, and also 7 by the division method, we will divide the numbers(2, 3, 7) by your prime determinants (preferably common). The product of this divisors provides the LCM of 2, 3, and 7.

Step 2: If any kind of of the offered numbers (2, 3, 7) is a many of 2, division it by 2 and write the quotient listed below it. Lug down any number the is no divisible by the prime number.Step 3: proceed the measures until just 1s are left in the last row.

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

☛ additionally Check:


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

Solution:

The value 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 also 7:

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, . . . ., 38, 40, 42, . . . .Multiples of 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 between the GCD and LCM of 2, 3, and also 7.

Solution:

The relation between GCD and LCM the 2, 3, and 7 is given as,LCM(2, 3, 7) = <(2 × 3 × 7) × GCD(2, 3, 7)>/⇒ prime factorization the 2, 3 and also 7:

2 = 213 = 317 = 71

∴ GCD the (2, 3), (3, 7), (2, 7) and also (2, 3, 7) = 1, 1, 1 and also 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 on LCM of 2, 3, and also 7

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

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

What room the methods to discover LCM of 2, 3, 7?

The typically used approaches to discover the LCM the 2, 3, 7 are:

Prime factorization MethodDivision MethodListing Multiples

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

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

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

The following equation can be supplied to express the relation in between GCF and also LCM of 2, 3, 7, i.e. LCM(2, 3, 7) = <(2 × 3 × 7) × GCF(2, 3, 7)>/.