LCM the 4, 6, and 9 is the the smallest number among all common multiples of 4, 6, and also 9. The first couple of multiples that 4, 6, and also 9 are (4, 8, 12, 16, 20 . . .), (6, 12, 18, 24, 30 . . .), and (9, 18, 27, 36, 45 . . .) respectively. There room 3 generally used approaches to uncover LCM of 4, 6, 9 - by department method, by element factorization, and also by listing multiples.

You are watching: What is the lcm of 4,6 and 9

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

Answer: LCM the 4, 6, and 9 is 36.

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Explanation:

The LCM of 3 non-zero integers, a(4), b(6), and c(9), is the smallest positive integer m(36) that is divisible through a(4), b(6), and c(9) without any remainder.


The approaches to discover the LCM the 4, 6, and also 9 are defined below.

By department MethodBy element Factorization MethodBy Listing Multiples

LCM of 4, 6, and 9 by department Method

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To calculation the LCM the 4, 6, and also 9 through the division method, we will divide the numbers(4, 6, 9) by your prime determinants (preferably common). The product of these divisors provides the LCM that 4, 6, and also 9.

Step 2: If any kind of of the given numbers (4, 6, 9) is a lot of of 2, division it by 2 and write the quotient listed below it. Carry down any number the is no divisible by the prime number.Step 3: continue the measures until only 1s space left in the last row.

The LCM the 4, 6, and also 9 is the product of every prime number on the left, i.e. LCM(4, 6, 9) by department method = 2 × 2 × 3 × 3 = 36.

LCM the 4, 6, and also 9 by element Factorization

Prime factorization of 4, 6, and also 9 is (2 × 2) = 22, (2 × 3) = 21 × 31, and also (3 × 3) = 32 respectively. LCM that 4, 6, and 9 have the right to be acquired by multiplying prime determinants raised to your respective highest power, i.e. 22 × 32 = 36.Hence, the LCM of 4, 6, and 9 by prime factorization is 36.

LCM of 4, 6, and also 9 by Listing Multiples

To calculate the LCM of 4, 6, 9 by listing out the usual multiples, we deserve to follow the given below steps:

Step 1: perform a couple of multiples that 4 (4, 8, 12, 16, 20 . . .), 6 (6, 12, 18, 24, 30 . . .), and also 9 (9, 18, 27, 36, 45 . . .).Step 2: The common multiples native the multiples of 4, 6, and 9 are 36, 72, . . .Step 3: The smallest typical multiple the 4, 6, and 9 is 36.

∴ The least usual multiple that 4, 6, and also 9 = 36.

☛ also Check:


Example 3: Verify the relationship between the GCD and LCM of 4, 6, and 9.

Solution:

The relation in between GCD and LCM that 4, 6, and 9 is given as,LCM(4, 6, 9) = <(4 × 6 × 9) × GCD(4, 6, 9)>/⇒ prime factorization of 4, 6 and 9:

4 = 226 = 21 × 319 = 32

∴ GCD the (4, 6), (6, 9), (4, 9) and also (4, 6, 9) = 2, 3, 1 and 1 respectively.Now, LHS = LCM(4, 6, 9) = 36.And, RHS = <(4 × 6 × 9) × GCD(4, 6, 9)>/ = <(216) × 1>/<2 × 3 × 1> = 36LHS = RHS = 36.Hence verified.


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FAQs on LCM of 4, 6, and also 9

What is the LCM of 4, 6, and also 9?

The LCM that 4, 6, and 9 is 36. To uncover the LCM (least usual multiple) that 4, 6, and 9, we require to find the multiples the 4, 6, and also 9 (multiples the 4 = 4, 8, 12, 16 . . . . 36 . . . . ; multiples of 6 = 6, 12, 18, 24, 36 . . . .; multiples of 9 = 9, 18, 27, 36 . . . .) and also choose the smallest multiple that is specifically divisible by 4, 6, and also 9, i.e., 36.

What is the the very least Perfect Square Divisible through 4, 6, and also 9?

The least number divisible by 4, 6, and 9 = LCM(4, 6, 9)LCM of 4, 6, and also 9 = 2 × 2 × 3 × 3 ⇒ the very least perfect square divisible by every 4, 6, and also 9 = LCM(4, 6, 9) = 36 Therefore, 36 is the compelled number.

Which of the adhering to is the LCM the 4, 6, and 9? 16, 52, 20, 36

The value of LCM that 4, 6, 9 is the smallest typical multiple that 4, 6, and 9. The number solve the given problem is 36.

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How to discover the LCM that 4, 6, and also 9 by prime Factorization?

To uncover the LCM that 4, 6, and 9 utilizing prime factorization, us will uncover the element factors, (4 = 22), (6 = 21 × 31), and also (9 = 32). LCM of 4, 6, and also 9 is the product that prime components raised to your respective greatest exponent among the numbers 4, 6, and also 9.⇒ LCM that 4, 6, 9 = 22 × 32 = 36.