LCM of 4, 5, and also 6 is the smallest number among all usual multiples that 4, 5, and 6. The first couple of multiples that 4, 5, and 6 room (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), and also (6, 12, 18, 24, 30 . . .) respectively. There space 3 typically used methods to uncover LCM that 4, 5, 6 - by division method, by prime factorization, and by listing multiples.

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

Answer: LCM of 4, 5, and 6 is 60.

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Explanation:

The LCM of 3 non-zero integers, a(4), b(5), and also c(6), is the smallest optimistic integer m(60) that is divisible by a(4), b(5), and c(6) without any kind of remainder.


Let's look at the various methods for finding the LCM that 4, 5, and 6.

By Listing MultiplesBy division MethodBy prime Factorization Method

LCM that 4, 5, and also 6 through Listing Multiples

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To calculation the LCM of 4, 5, 6 by listing the end the typical multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples of 4 (4, 8, 12, 16, 20 . . .), 5 (5, 10, 15, 20, 25 . . .), and 6 (6, 12, 18, 24, 30 . . .).Step 2: The typical multiples native the multiples of 4, 5, and also 6 are 60, 120, . . .Step 3: The smallest common multiple the 4, 5, and 6 is 60.

∴ The least usual multiple of 4, 5, and 6 = 60.

LCM the 4, 5, and 6 by department Method

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To calculation the LCM the 4, 5, and 6 by the department method, we will certainly divide the numbers(4, 5, 6) by your prime determinants (preferably common). The product of these divisors offers the LCM that 4, 5, and 6.

Step 2: If any type of of the offered numbers (4, 5, 6) is a many of 2, division it through 2 and also write the quotient listed below it. Bring down any type of number the is not divisible by the prime number.Step 3: continue the steps until only 1s are left in the last row.

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

LCM that 4, 5, and 6 by element Factorization

Prime administer of 4, 5, and also 6 is (2 × 2) = 22, (5) = 51, and also (2 × 3) = 21 × 31 respectively. LCM of 4, 5, and 6 have the right to be derived by multiply prime factors raised to your respective greatest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM of 4, 5, and 6 by element factorization is 60.

☛ likewise Check:


Example 2: Verify the relationship in between the GCD and LCM the 4, 5, and 6.

Solution:

The relation between GCD and also LCM of 4, 5, and 6 is provided as,LCM(4, 5, 6) = <(4 × 5 × 6) × GCD(4, 5, 6)>/⇒ element factorization of 4, 5 and also 6:

4 = 225 = 516 = 21 × 31

∴ GCD the (4, 5), (5, 6), (4, 6) and also (4, 5, 6) = 1, 1, 2 and 1 respectively.Now, LHS = LCM(4, 5, 6) = 60.And, RHS = <(4 × 5 × 6) × GCD(4, 5, 6)>/ = <(120) × 1>/<1 × 1 × 2> = 60LHS = RHS = 60.Hence verified.


Example 3: calculate the LCM the 4, 5, and 6 using the GCD the the provided numbers.

Solution:

Prime administrate of 4, 5, 6:

4 = 225 = 516 = 21 × 31

Therefore, GCD(4, 5) = 1, GCD(5, 6) = 1, GCD(4, 6) = 2, GCD(4, 5, 6) = 1We know,LCM(4, 5, 6) = <(4 × 5 × 6) × GCD(4, 5, 6)>/LCM(4, 5, 6) = (120 × 1)/(1 × 1 × 2) = 60⇒LCM(4, 5, 6) = 60


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FAQs ~ above LCM of 4, 5, and 6

What is the LCM the 4, 5, and also 6?

The LCM the 4, 5, and also 6 is 60. To find the least common multiple (LCM) that 4, 5, and 6, we need to uncover the multiples the 4, 5, and 6 (multiples of 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples the 5 = 5, 10, 15, 20 . . . . 60 . . . . ; multiples of 6 = 6, 12, 18, 24 . . . . 60 . . . . ) and choose the smallest multiple that is specifically divisible through 4, 5, and 6, i.e., 60.

What is the least Perfect Square Divisible by 4, 5, and 6?

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

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What are the approaches to uncover LCM that 4, 5, 6?

The typically used techniques to uncover the LCM the 4, 5, 6 are:

Division MethodListing MultiplesPrime administrate Method

How to find the LCM the 4, 5, and also 6 by element Factorization?

To uncover the LCM the 4, 5, and also 6 utilizing prime factorization, we will discover the element factors, (4 = 22), (5 = 51), and also (6 = 21 × 31). LCM of 4, 5, and 6 is the product that prime determinants raised to their respective greatest exponent amongst the number 4, 5, and also 6.⇒ LCM that 4, 5, 6 = 22 × 31 × 51 = 60.