LCM of 16, 24, and also 40 is the smallest number amongst all typical multiples of 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 (40, 80, 120, 160, 200 . . .) respectively. There room 3 generally used approaches to discover LCM that 16, 24, 40 - through listing multiples, by division method, and by prime factorization.

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

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

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Explanation:

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


The techniques to uncover the LCM of 16, 24, and 40 are described below.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM of 16, 24, and also 40 by department Method

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To calculate the LCM that 16, 24, and also 40 by the department method, we will certainly divide the numbers(16, 24, 40) by their prime determinants (preferably common). The product of this divisors offers the LCM the 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 also write the quotient listed below it. Bring down any type of number that is not divisible by the prime number.Step 3: proceed the steps until just 1s room left in the last row.

The LCM of 16, 24, and also 40 is the product of every prime numbers 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 that 16, 24, and 40 deserve to be acquired by multiply prime components raised to their respective greatest power, i.e. 24 × 31 × 51 = 240.Hence, the LCM the 16, 24, and 40 by element factorization is 240.

LCM the 16, 24, and also 40 through Listing Multiples

To calculate the LCM the 16, 24, 40 by listing out the typical multiples, we can 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 usual multiples indigenous the multiples that 16, 24, and also 40 are 240, 480, . . .Step 3: The smallest usual multiple the 16, 24, and 40 is 240.

∴ The least typical multiple the 16, 24, and also 40 = 240.

☛ also Check:


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

Solution:

The relation in between GCD and also LCM that 16, 24, and also 40 is given as,LCM(16, 24, 40) = <(16 × 24 × 40) × GCD(16, 24, 40)>/⇒ prime factorization the 16, 24 and also 40:

16 = 2424 = 23 × 3140 = 23 × 51

∴ GCD the (16, 24), (24, 40), (16, 40) and also (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 that 16, 24, and also 40

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

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

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

The typically used methods to find the LCM that 16, 24, 40 are:

Prime factorization MethodDivision MethodListing Multiples

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

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

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

The complying with equation have the right to be provided to refer the relation between GCF and LCM of 16, 24, 40, i.e. LCM(16, 24, 40) = <(16 × 24 × 40) × GCF(16, 24, 40)>/.