LCM the 5, 6, and 9 is the smallest number amongst all usual multiples the 5, 6, and 9. The first couple of multiples the 5, 6, and also 9 space (5, 10, 15, 20, 25 . . .), (6, 12, 18, 24, 30 . . .), and also (9, 18, 27, 36, 45 . . .) respectively. There room 3 generally used approaches to discover LCM the 5, 6, 9 - by element factorization, by listing multiples, and by department method.

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1.LCM the 5, 6, and 9
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 5, 6, and 9 is 90.

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Explanation:

The LCM of three non-zero integers, a(5), b(6), and also c(9), is the smallest confident integer m(90) the is divisible through a(5), b(6), and c(9) without any type of remainder.


Let's look in ~ the various methods for finding the LCM of 5, 6, and also 9.

By Listing MultiplesBy element Factorization MethodBy department Method

LCM that 5, 6, and also 9 by Listing Multiples

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To calculation the LCM the 5, 6, 9 by listing the end the common multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples of 5 (5, 10, 15, 20, 25 . . .), 6 (6, 12, 18, 24, 30 . . .), and also 9 (9, 18, 27, 36, 45 . . .).Step 2: The typical multiples native the multiples the 5, 6, and 9 room 90, 180, . . .Step 3: The smallest typical multiple the 5, 6, and also 9 is 90.

∴ The least usual multiple of 5, 6, and also 9 = 90.

LCM of 5, 6, and also 9 by prime Factorization

Prime factorization of 5, 6, and also 9 is (5) = 51, (2 × 3) = 21 × 31, and (3 × 3) = 32 respectively. LCM that 5, 6, and 9 deserve to be obtained by multiplying prime determinants raised to your respective highest possible power, i.e. 21 × 32 × 51 = 90.Hence, the LCM of 5, 6, and 9 by prime factorization is 90.

LCM the 5, 6, and also 9 by division Method

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To calculation the LCM the 5, 6, and also 9 through the department method, we will certainly divide the numbers(5, 6, 9) by your prime components (preferably common). The product of these divisors provides the LCM of 5, 6, and also 9.

Step 2: If any type of of the provided numbers (5, 6, 9) is a lot of of 2, division it by 2 and also write the quotient below it. Carry down any number the is not divisible by the element number.Step 3: proceed the steps until only 1s are left in the critical row.

The LCM the 5, 6, and 9 is the product of all prime number on the left, i.e. LCM(5, 6, 9) by department method = 2 × 3 × 3 × 5 = 90.

☛ additionally Check:


Example 1: Verify the relationship in between the GCD and LCM the 5, 6, and also 9.

Solution:

The relation in between GCD and also LCM that 5, 6, and 9 is provided as,LCM(5, 6, 9) = <(5 × 6 × 9) × GCD(5, 6, 9)>/⇒ prime factorization that 5, 6 and also 9:

5 = 516 = 21 × 319 = 32

∴ GCD of (5, 6), (6, 9), (5, 9) and also (5, 6, 9) = 1, 3, 1 and also 1 respectively.Now, LHS = LCM(5, 6, 9) = 90.And, RHS = <(5 × 6 × 9) × GCD(5, 6, 9)>/ = <(270) × 1>/<1 × 3 × 1> = 90LHS = RHS = 90.Hence verified.


Example 2: discover the the smallest number that is divisible by 5, 6, 9 exactly.

Solution:

The worth of LCM(5, 6, 9) will be the smallest number the is precisely divisible by 5, 6, and also 9.⇒ Multiples the 5, 6, and 9:

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 75, 80, 85, 90, . . . .Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 72, 78, 84, 90, . . . .Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 72, 81, 90, . . . .

Therefore, the LCM of 5, 6, and 9 is 90.


Example 3: calculate the LCM of 5, 6, and 9 utilizing the GCD that the given numbers.

Solution:

Prime factorization of 5, 6, 9:

5 = 516 = 21 × 319 = 32

Therefore, GCD(5, 6) = 1, GCD(6, 9) = 3, GCD(5, 9) = 1, GCD(5, 6, 9) = 1We know,LCM(5, 6, 9) = <(5 × 6 × 9) × GCD(5, 6, 9)>/LCM(5, 6, 9) = (270 × 1)/(1 × 3 × 1) = 90⇒LCM(5, 6, 9) = 90


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FAQs top top LCM of 5, 6, and 9

What is the LCM the 5, 6, and 9?

The LCM of 5, 6, and also 9 is 90. To uncover the LCM (least common multiple) of 5, 6, and also 9, we require to discover the multiples of 5, 6, and also 9 (multiples of 5 = 5, 10, 15, 20 . . . . 90 . . . . ; multiples that 6 = 6, 12, 18, 24 . . . . 90 . . . . ; multiples of 9 = 9, 18, 27, 36 . . . . 90 . . . . ) and choose the the smallest multiple that is exactly divisible by 5, 6, and 9, i.e., 90.

Which the the adhering to is the LCM that 5, 6, and 9? 50, 90, 100, 5

The value of LCM of 5, 6, 9 is the smallest usual multiple of 5, 6, and also 9. The number satisfying the given problem is 90.

How to uncover the LCM that 5, 6, and also 9 by prime Factorization?

To find the LCM the 5, 6, and 9 using prime factorization, we will find the element factors, (5 = 51), (6 = 21 × 31), and also (9 = 32). LCM of 5, 6, and also 9 is the product that prime components raised to your respective highest possible exponent among the numbers 5, 6, and also 9.⇒ LCM that 5, 6, 9 = 21 × 32 × 51 = 90.

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What is the Relation in between GCF and also LCM the 5, 6, 9?

The complying with equation have the right to be used to express the relation between GCF and also LCM that 5, 6, 9, i.e. LCM(5, 6, 9) = <(5 × 6 × 9) × GCF(5, 6, 9)>/.