LCM the 4, 5, and also 6 is the smallest number amongst all typical multiples of 4, 5, and also 6. The first few multiples the 4, 5, and 6 space (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), and (6, 12, 18, 24, 30 . . .) respectively. There space 3 frequently used techniques to discover LCM that 4, 5, 6 - by department method, by prime factorization, and by listing multiples.

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

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

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Explanation:

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


Let's look in ~ the different methods because that finding the LCM of 4, 5, and 6.

By Listing MultiplesBy division MethodBy prime Factorization Method

LCM that 4, 5, and 6 by Listing Multiples

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To calculate the LCM of 4, 5, 6 by listing out the common multiples, we deserve to follow the given listed below steps:

Step 1: list a few multiples the 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 that 4, 5, and 6 room 60, 120, . . .Step 3: The smallest typical multiple the 4, 5, and also 6 is 60.

∴ The least common multiple that 4, 5, and 6 = 60.

LCM the 4, 5, and 6 by division Method

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To calculate the LCM the 4, 5, and 6 by the division method, we will divide the numbers(4, 5, 6) by their prime factors (preferably common). The product of this divisors offers the LCM the 4, 5, and 6.

Step 2: If any of the given numbers (4, 5, 6) is a lot of of 2, division it by 2 and write the quotient listed below it. Lug down any number that is not divisible by the element number.Step 3: continue the measures until just 1s room left in the last row.

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

LCM the 4, 5, and also 6 by element Factorization

Prime administrate of 4, 5, and also 6 is (2 × 2) = 22, (5) = 51, and also (2 × 3) = 21 × 31 respectively. LCM that 4, 5, and 6 deserve to be obtained by multiply prime determinants raised to your respective highest possible power, i.e. 22 × 31 × 51 = 60.Hence, the LCM of 4, 5, and 6 by prime factorization is 60.

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

Solution:

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

4 = 225 = 516 = 21 × 31

∴ GCD of (4, 5), (5, 6), (4, 6) and also (4, 5, 6) = 1, 1, 2 and also 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: calculation the LCM that 4, 5, and also 6 using the GCD the the given numbers.

Solution:

Prime administer 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 on LCM of 4, 5, and also 6

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

The LCM that 4, 5, and also 6 is 60. To discover the least usual multiple (LCM) that 4, 5, and 6, we require to discover the multiples that 4, 5, and 6 (multiples of 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples of 5 = 5, 10, 15, 20 . . . . 60 . . . . ; multiples that 6 = 6, 12, 18, 24 . . . . 60 . . . . ) and choose the the smallest multiple that is precisely divisible by 4, 5, and 6, i.e., 60.

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

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

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What space the approaches to uncover LCM the 4, 5, 6?

The frequently used techniques to discover the LCM of 4, 5, 6 are:

Division MethodListing MultiplesPrime factorization Method

How to uncover the LCM of 4, 5, and 6 by element Factorization?

To uncover the LCM of 4, 5, and also 6 utilizing prime factorization, us will uncover the prime factors, (4 = 22), (5 = 51), and also (6 = 21 × 31). LCM of 4, 5, and 6 is the product of prime components raised to their respective highest possible exponent among the number 4, 5, and 6.⇒ LCM the 4, 5, 6 = 22 × 31 × 51 = 60.