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. 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 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 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.

☛ also Check:

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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go come slidego come slidego to slide ## 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.