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

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

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

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Explanation:

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


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

By Listing MultiplesBy element Factorization MethodBy division Method

LCM of 5, 6, and 9 by Listing Multiples

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To calculate the LCM the 5, 6, 9 through listing out the usual multiples, we have the right to follow the given listed below steps:

Step 1: list a few 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 indigenous the multiples the 5, 6, and also 9 space 90, 180, . . .Step 3: The smallest typical multiple of 5, 6, and 9 is 90.

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

LCM the 5, 6, and also 9 by element Factorization

Prime administrate of 5, 6, and 9 is (5) = 51, (2 × 3) = 21 × 31, and also (3 × 3) = 32 respectively. LCM the 5, 6, and 9 deserve to be acquired by multiplying prime components raised to your respective greatest power, i.e. 21 × 32 × 51 = 90.Hence, the LCM of 5, 6, and also 9 by element factorization is 90.

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

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To calculate the LCM the 5, 6, and 9 by the division method, we will certainly divide the numbers(5, 6, 9) by their prime determinants (preferably common). The product of this divisors provides the LCM of 5, 6, and 9.

Step 2: If any of the offered numbers (5, 6, 9) is a lot of of 2, divide it through 2 and also write the quotient below it. Bring down any number the is no divisible through the element number.Step 3: proceed the procedures until just 1s room left in the last row.

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

☛ additionally Check:


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

Solution:

The relation between GCD and LCM the 5, 6, and 9 is given as,LCM(5, 6, 9) = <(5 × 6 × 9) × GCD(5, 6, 9)>/⇒ element factorization of 5, 6 and also 9:

5 = 516 = 21 × 319 = 32

∴ GCD the (5, 6), (6, 9), (5, 9) and also (5, 6, 9) = 1, 3, 1 and 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: uncover the the smallest number the is divisible by 5, 6, 9 exactly.

Solution:

The worth of LCM(5, 6, 9) will certainly be the smallest number the is specifically divisible through 5, 6, and 9.⇒ Multiples the 5, 6, and 9:

Multiples the 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 that 5, 6, and also 9 is 90.


Example 3: calculation the LCM the 5, 6, and 9 using the GCD the the offered 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 on 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) the 5, 6, and also 9, we need to discover the multiples of 5, 6, and also 9 (multiples of 5 = 5, 10, 15, 20 . . . . 90 . . . . ; multiples of 6 = 6, 12, 18, 24 . . . . 90 . . . . ; multiples the 9 = 9, 18, 27, 36 . . . . 90 . . . . ) and choose the smallest multiple that is exactly divisible through 5, 6, and also 9, i.e., 90.

Which that the following is the LCM that 5, 6, and also 9? 50, 90, 100, 5

The value of LCM that 5, 6, 9 is the smallest typical multiple that 5, 6, and 9. The number solve the given problem is 90.

How to find the LCM the 5, 6, and 9 by prime Factorization?

To find the LCM of 5, 6, and also 9 making use of prime factorization, us will discover the prime factors, (5 = 51), (6 = 21 × 31), and also (9 = 32). LCM of 5, 6, and also 9 is the product that prime determinants raised to their respective highest exponent among the number 5, 6, and also 9.⇒ LCM of 5, 6, 9 = 21 × 32 × 51 = 90.

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

The adhering to equation deserve to be provided to refer the relation in between GCF and LCM of 5, 6, 9, i.e. LCM(5, 6, 9) = <(5 × 6 × 9) × GCF(5, 6, 9)>/.