LCM the 3, 5, and also 9 is the the smallest number amongst all typical multiples of 3, 5, and 9. The first few multiples that 3, 5, and 9 are (3, 6, 9, 12, 15 . . .), (5, 10, 15, 20, 25 . . .), and (9, 18, 27, 36, 45 . . .) respectively. There room 3 typically used methods to uncover LCM the 3, 5, 9 - by element factorization, by listing multiples, and by department method.

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

Answer: LCM that 3, 5, and also 9 is 45.

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Explanation:

The LCM of 3 non-zero integers, a(3), b(5), and c(9), is the smallest positive integer m(45) that is divisible through a(3), b(5), and also c(9) without any type of remainder.


The techniques to discover the LCM that 3, 5, and also 9 are explained below.

By prime Factorization MethodBy Listing MultiplesBy division Method

LCM the 3, 5, and also 9 by prime Factorization

Prime factorization of 3, 5, and 9 is (3) = 31, (5) = 51, and (3 × 3) = 32 respectively. LCM the 3, 5, and also 9 have the right to be derived by multiplying prime components raised to your respective highest possible power, i.e. 32 × 51 = 45.Hence, the LCM of 3, 5, and also 9 by element factorization is 45.

LCM of 3, 5, and also 9 by Listing Multiples

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To calculate the LCM the 3, 5, 9 through listing the end the typical multiples, we have the right to follow the given listed below steps:

Step 1: perform a few multiples the 3 (3, 6, 9, 12, 15 . . .), 5 (5, 10, 15, 20, 25 . . .), and 9 (9, 18, 27, 36, 45 . . .).Step 2: The common multiples from the multiples that 3, 5, and 9 are 45, 90, . . .Step 3: The smallest typical multiple that 3, 5, and also 9 is 45.

∴ The least common multiple the 3, 5, and 9 = 45.

LCM of 3, 5, and also 9 by department Method

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To calculation the LCM the 3, 5, and 9 by the department method, we will divide the numbers(3, 5, 9) by their prime factors (preferably common). The product of these divisors provides the LCM of 3, 5, and 9.

Step 2: If any of the given numbers (3, 5, 9) is a many of 3, divide it by 3 and write the quotient listed below it. Carry down any type of number the is not divisible by the prime number.Step 3: proceed the procedures until only 1s are left in the critical row.

The LCM of 3, 5, and 9 is the product of every prime number on the left, i.e. LCM(3, 5, 9) by department method = 3 × 3 × 5 = 45.

☛ also Check:


Example 2: Verify the relationship in between the GCD and LCM that 3, 5, and 9.

Solution:

The relation between GCD and LCM of 3, 5, and 9 is offered as,LCM(3, 5, 9) = <(3 × 5 × 9) × GCD(3, 5, 9)>/⇒ element factorization of 3, 5 and also 9:

3 = 315 = 519 = 32

∴ GCD the (3, 5), (5, 9), (3, 9) and (3, 5, 9) = 1, 1, 3 and also 1 respectively.Now, LHS = LCM(3, 5, 9) = 45.And, RHS = <(3 × 5 × 9) × GCD(3, 5, 9)>/ = <(135) × 1>/<1 × 1 × 3> = 45LHS = RHS = 45.Hence verified.


Example 3: find the smallest number that is divisible through 3, 5, 9 exactly.

Solution:

The the smallest number the is divisible through 3, 5, and 9 specifically is your LCM.⇒ Multiples of 3, 5, and 9:

Multiples the 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, . . . .Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, . . . .Multiples the 9 = 9, 18, 27, 36, 45, 54, . . . .

Therefore, the LCM of 3, 5, and 9 is 45.


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FAQs on LCM of 3, 5, and 9

What is the LCM the 3, 5, and also 9?

The LCM that 3, 5, and 9 is 45. To find the LCM (least typical multiple) the 3, 5, and also 9, we need to uncover the multiples of 3, 5, and 9 (multiples the 3 = 3, 6, 9, 12 . . . . 45 . . . . ; multiples the 5 = 5, 10, 15, 20 . . . . 45 . . . . ; multiples of 9 = 9, 18, 27, 36 . . . . 45 . . . . ) and choose the the smallest multiple the is exactly divisible by 3, 5, and also 9, i.e., 45.

What is the Relation between GCF and LCM of 3, 5, 9?

The complying with equation can be provided to express the relation between GCF and LCM of 3, 5, 9, i.e. LCM(3, 5, 9) = <(3 × 5 × 9) × GCF(3, 5, 9)>/.

Which that the complying with is the LCM of 3, 5, and 9? 81, 45, 21, 120

The worth of LCM that 3, 5, 9 is the smallest common multiple that 3, 5, and also 9. The number solve the given problem is 45.

See more: How Did Mendeleev Organize His Periodic Table ? Mendeleev'S Periodic Table

How to discover the LCM that 3, 5, and 9 by prime Factorization?

To discover the LCM the 3, 5, and also 9 making use of prime factorization, we will uncover the element factors, (3 = 31), (5 = 51), and also (9 = 32). LCM of 3, 5, and 9 is the product that prime components raised to your respective highest possible exponent amongst the number 3, 5, and 9.⇒ LCM the 3, 5, 9 = 32 × 51 = 45.