LCM that 16, 24, and also 40 is the the smallest number amongst all common multiples that 16, 24, and 40. The first few multiples the 16, 24, and also 40 room (16, 32, 48, 64, 80 . . .), (24, 48, 72, 96, 120 . . .), and also (40, 80, 120, 160, 200 . . .) respectively. There space 3 frequently used methods to uncover LCM of 16, 24, 40 - by listing multiples, by department method, and also by prime factorization.

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1.LCM that 16, 24, and also 40
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 16, 24, and also 40 is 240.

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Explanation:

The LCM of 3 non-zero integers, a(16), b(24), and c(40), is the smallest confident integer m(240) that is divisible by a(16), b(24), and c(40) without any type of remainder.


The approaches to find the LCM the 16, 24, and 40 are defined below.

By division MethodBy element Factorization MethodBy Listing Multiples

LCM the 16, 24, and 40 by department Method

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To calculate the LCM that 16, 24, and 40 through the division method, we will divide the numbers(16, 24, 40) by their prime components (preferably common). The product of this divisors provides the LCM that 16, 24, and also 40.

Step 2: If any of the offered numbers (16, 24, 40) is a multiple of 2, divide it by 2 and write the quotient listed below it. Bring down any type of number the is no divisible through the prime number.Step 3: proceed the steps until only 1s space left in the last row.

The LCM that 16, 24, and also 40 is the product of every prime number on the left, i.e. LCM(16, 24, 40) by department method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

LCM the 16, 24, and 40 by element Factorization

Prime factorization of 16, 24, and also 40 is (2 × 2 × 2 × 2) = 24, (2 × 2 × 2 × 3) = 23 × 31, and also (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM of 16, 24, and 40 have the right to be acquired by multiplying prime components raised to their respective highest power, i.e. 24 × 31 × 51 = 240.Hence, the LCM that 16, 24, and 40 by prime factorization is 240.

LCM the 16, 24, and 40 by Listing Multiples

To calculate the LCM the 16, 24, 40 through listing the end the common multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples the 16 (16, 32, 48, 64, 80 . . .), 24 (24, 48, 72, 96, 120 . . .), and also 40 (40, 80, 120, 160, 200 . . .).Step 2: The typical multiples indigenous the multiples the 16, 24, and also 40 are 240, 480, . . .Step 3: The smallest usual multiple of 16, 24, and 40 is 240.

∴ The least usual multiple that 16, 24, and also 40 = 240.

☛ likewise Check:


Example 3: Verify the relationship between the GCD and LCM that 16, 24, and also 40.

Solution:

The relation between GCD and also LCM of 16, 24, and 40 is provided as,LCM(16, 24, 40) = <(16 × 24 × 40) × GCD(16, 24, 40)>/⇒ element factorization of 16, 24 and 40:

16 = 2424 = 23 × 3140 = 23 × 51

∴ GCD the (16, 24), (24, 40), (16, 40) and (16, 24, 40) = 8, 8, 8 and also 8 respectively.Now, LHS = LCM(16, 24, 40) = 240.And, RHS = <(16 × 24 × 40) × GCD(16, 24, 40)>/ = <(15360) × 8>/<8 × 8 × 8> = 240LHS = RHS = 240.Hence verified.


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FAQs top top LCM the 16, 24, and 40

What is the LCM of 16, 24, and also 40?

The LCM that 16, 24, and 40 is 240. To discover the least usual multiple (LCM) the 16, 24, and also 40, we need to uncover the multiples the 16, 24, and also 40 (multiples of 16 = 16, 32, 48, 64 . . . . 240 . . . . ; multiples that 24 = 24, 48, 72, 96 . . . . 240 . . . . ; multiples the 40 = 40, 80, 120, 160, 240 . . . .) and also choose the the smallest multiple that is precisely divisible by 16, 24, and 40, i.e., 240.

What space the techniques to uncover LCM the 16, 24, 40?

The generally used approaches to discover the LCM of 16, 24, 40 are:

Prime factorization MethodDivision MethodListing Multiples

What is the the very least Perfect Square Divisible by 16, 24, and 40?

The least number divisible through 16, 24, and 40 = LCM(16, 24, 40)LCM of 16, 24, and 40 = 2 × 2 × 2 × 2 × 3 × 5 ⇒ least perfect square divisible by each 16, 24, and 40 = LCM(16, 24, 40) × 3 × 5 = 3600 Therefore, 3600 is the required number.

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What is the Relation in between GCF and also LCM of 16, 24, 40?

The following equation can be provided to express the relation between GCF and LCM that 16, 24, 40, i.e. LCM(16, 24, 40) = <(16 × 24 × 40) × GCF(16, 24, 40)>/.