LCM the 4, 6, and also 10 is the smallest number amongst all typical multiples of 4, 6, and 10. The first few multiples the 4, 6, and also 10 are (4, 8, 12, 16, 20 . . .), (6, 12, 18, 24, 30 . . .), and also (10, 20, 30, 40, 50 . . .) respectively. There space 3 frequently used methods to uncover LCM the 4, 6, 10 - by listing multiples, by element factorization, and also by department method.

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1.LCM of 4, 6, and also 10
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 4, 6, and also 10 is 60.

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Explanation:

The LCM of three non-zero integers, a(4), b(6), and also c(10), is the smallest positive integer m(60) the is divisible by a(4), b(6), and also c(10) without any kind of remainder.


Let's look at the various methods because that finding the LCM of 4, 6, and also 10.

By Listing MultiplesBy department MethodBy element Factorization Method

LCM that 4, 6, and 10 through Listing Multiples

To calculation the LCM of 4, 6, 10 by listing out the typical multiples, we deserve to follow the given listed below steps:

Step 1: perform a few multiples that 4 (4, 8, 12, 16, 20 . . .), 6 (6, 12, 18, 24, 30 . . .), and also 10 (10, 20, 30, 40, 50 . . .).Step 2: The usual multiples from the multiples that 4, 6, and 10 space 60, 120, . . .Step 3: The smallest common multiple that 4, 6, and also 10 is 60.

∴ The least typical multiple that 4, 6, and also 10 = 60.

LCM the 4, 6, and also 10 by department Method

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To calculate the LCM of 4, 6, and 10 through the department method, we will certainly divide the numbers(4, 6, 10) by their prime components (preferably common). The product of this divisors gives the LCM that 4, 6, and also 10.

Step 2: If any of the provided numbers (4, 6, 10) is a lot of of 2, division it by 2 and write the quotient listed below it. Carry down any kind of number the is no divisible by the element number.Step 3: proceed the actions until just 1s are left in the critical row.

The LCM that 4, 6, and 10 is the product of every prime numbers on the left, i.e. LCM(4, 6, 10) by department method = 2 × 2 × 3 × 5 = 60.

LCM that 4, 6, and also 10 by prime Factorization

Prime administrate of 4, 6, and 10 is (2 × 2) = 22, (2 × 3) = 21 × 31, and (2 × 5) = 21 × 51 respectively. LCM that 4, 6, and 10 have the right to be acquired by multiplying prime factors raised to your respective highest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM the 4, 6, and 10 by element factorization is 60.

☛ also Check:


Example 3: Verify the relationship between the GCD and LCM the 4, 6, and 10.

Solution:

The relation between GCD and also LCM of 4, 6, and also 10 is offered as,LCM(4, 6, 10) = <(4 × 6 × 10) × GCD(4, 6, 10)>/⇒ prime factorization of 4, 6 and also 10:

4 = 226 = 21 × 3110 = 21 × 51

∴ GCD the (4, 6), (6, 10), (4, 10) and (4, 6, 10) = 2, 2, 2 and 2 respectively.Now, LHS = LCM(4, 6, 10) = 60.And, RHS = <(4 × 6 × 10) × GCD(4, 6, 10)>/ = <(240) × 2>/<2 × 2 × 2> = 60LHS = RHS = 60.Hence verified.


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FAQs on LCM of 4, 6, and also 10

What is the LCM of 4, 6, and also 10?

The LCM that 4, 6, and 10 is 60. To discover the LCM (least common multiple) of 4, 6, and 10, we need to find the multiples that 4, 6, and also 10 (multiples the 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples that 6 = 6, 12, 18, 24 . . . . 60 . . . . ; multiples of 10 = 10, 20, 30, 40, 60 . . . .) and choose the the smallest multiple the is precisely divisible by 4, 6, and 10, i.e., 60.

What is the least Perfect Square Divisible by 4, 6, and 10?

The the very least number divisible through 4, 6, and also 10 = LCM(4, 6, 10)LCM of 4, 6, and 10 = 2 × 2 × 3 × 5 ⇒ the very least perfect square divisible by every 4, 6, and also 10 = LCM(4, 6, 10) × 3 × 5 = 900 Therefore, 900 is the forced number.

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What is the Relation in between GCF and LCM that 4, 6, 10?

The adhering to equation can be supplied to refer the relation in between GCF and also LCM of 4, 6, 10, i.e. LCM(4, 6, 10) = <(4 × 6 × 10) × GCF(4, 6, 10)>/.

What room the techniques to uncover LCM the 4, 6, 10?

The frequently used approaches to find the LCM the 4, 6, 10 are: