LCM that 16 and also 24 is the the smallest number among all usual multiples the 16 and also 24. The first couple of multiples of 16 and also 24 space (16, 32, 48, 64, 80, 96, . . . ) and (24, 48, 72, 96, 120, 144, 168, . . . ) respectively. There are 3 typically used techniques to uncover LCM that 16 and 24 - by prime factorization, through listing multiples, and also by department method.

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1.LCM of 16 and 24
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 16 and also 24 is 48.

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Explanation:

The LCM of 2 non-zero integers, x(16) and also y(24), is the smallest confident integer m(48) that is divisible through both x(16) and y(24) without any kind of remainder.


Let's look at the different methods because that finding the LCM the 16 and also 24.

By department MethodBy element Factorization MethodBy Listing Multiples

LCM that 16 and also 24 by department Method

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To calculate the LCM that 16 and 24 by the department method, we will divide the numbers(16, 24) by your prime components (preferably common). The product of this divisors offers the LCM the 16 and also 24.

Step 3: continue the measures until just 1s are left in the last row.

The LCM of 16 and 24 is the product of all prime numbers on the left, i.e. LCM(16, 24) by division method = 2 × 2 × 2 × 2 × 3 = 48.

LCM of 16 and also 24 by prime Factorization

Prime administer of 16 and 24 is (2 × 2 × 2 × 2) = 24 and (2 × 2 × 2 × 3) = 23 × 31 respectively. LCM the 16 and also 24 can be derived by multiply prime factors raised to their respective highest possible power, i.e. 24 × 31 = 48.Hence, the LCM of 16 and also 24 by prime factorization is 48.

LCM that 16 and 24 through Listing Multiples

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To calculate the LCM that 16 and also 24 through listing the end the typical multiples, we can follow the given below steps:

Step 1: list a couple of multiples of 16 (16, 32, 48, 64, 80, 96, . . . ) and also 24 (24, 48, 72, 96, 120, 144, 168, . . . . )Step 2: The common multiples from the multiples the 16 and also 24 are 48, 96, . . .Step 3: The smallest usual multiple the 16 and also 24 is 48.

∴ The least usual multiple that 16 and also 24 = 48.

☛ also Check:


Example 1: Verify the relationship in between GCF and also LCM that 16 and also 24.

Solution:

The relation in between GCF and also LCM of 16 and 24 is provided as,LCM(16, 24) × GCF(16, 24) = Product the 16, 24Prime administrate of 16 and 24 is provided as, 16 = (2 × 2 × 2 × 2) = 24 and 24 = (2 × 2 × 2 × 3) = 23 × 31LCM(16, 24) = 48GCF(16, 24) = 8LHS = LCM(16, 24) × GCF(16, 24) = 48 × 8 = 384RHS = Product of 16, 24 = 16 × 24 = 384⇒ LHS = RHS = 384Hence, verified.


Example 2: The product of 2 numbers is 384. If their GCD is 8, what is your LCM?

Solution:

Given: GCD = 8product of number = 384∵ LCM × GCD = product the numbers⇒ LCM = Product/GCD = 384/8Therefore, the LCM is 48.The probable combination for the given instance is LCM(16, 24) = 48.


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FAQs ~ above LCM of 16 and 24

What is the LCM the 16 and 24?

The LCM of 16 and 24 is 48. To uncover the LCM of 16 and 24, we require to uncover the multiples of 16 and also 24 (multiples that 16 = 16, 32, 48, 64; multiples of 24 = 24, 48, 72, 96) and choose the the smallest multiple the is specifically divisible through 16 and 24, i.e., 48.

What is the least Perfect Square Divisible through 16 and 24?

The the very least number divisible by 16 and also 24 = LCM(16, 24)LCM that 16 and also 24 = 2 × 2 × 2 × 2 × 3 ⇒ the very least perfect square divisible by every 16 and 24 = LCM(16, 24) × 3 = 144 Therefore, 144 is the forced number.

If the LCM that 24 and also 16 is 48, discover its GCF.

LCM(24, 16) × GCF(24, 16) = 24 × 16Since the LCM that 24 and also 16 = 48⇒ 48 × GCF(24, 16) = 384Therefore, the greatest usual factor = 384/48 = 8.

Which that the adhering to is the LCM that 16 and 24? 30, 42, 21, 48

The value of LCM of 16, 24 is the smallest common multiple the 16 and 24. The number satisfying the given condition is 48.

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

The adhering to equation deserve to be used to to express the relation between GCF and also LCM the 16 and also 24, i.e. GCF × LCM = 16 × 24.