LCM of 16 and 24 is the the smallest number amongst all usual multiples that 16 and 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 generally used methods to uncover LCM the 16 and also 24 - by prime factorization, by listing multiples, and also by department method.

You are watching: Least common factor of 16 and 24

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

Answer: LCM of 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 hopeful integer m(48) the is divisible through both x(16) and y(24) without any kind of remainder.


Let's look in ~ the various methods for finding the LCM that 16 and also 24.

By department MethodBy element Factorization MethodBy Listing Multiples

LCM the 16 and also 24 by department Method

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

Step 3: proceed the procedures until only 1s space left in the critical row.

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

LCM that 16 and 24 by element Factorization

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

LCM that 16 and 24 through Listing Multiples

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To calculate the LCM of 16 and 24 by listing the end the usual multiples, we can follow the given listed below steps:

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

∴ The least common multiple the 16 and 24 = 48.

☛ also Check:


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

Solution:

The relation in between GCF and LCM of 16 and 24 is provided as,LCM(16, 24) × GCF(16, 24) = Product the 16, 24Prime administrate of 16 and 24 is given 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 that 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 their LCM?

Solution:

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


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FAQs on LCM of 16 and also 24

What is the LCM the 16 and also 24?

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

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

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

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

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

Which of the complying with is the LCM of 16 and also 24? 30, 42, 21, 48

The worth of LCM the 16, 24 is the smallest usual multiple the 16 and 24. The number to solve the given problem is 48.

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

The following equation have the right to be supplied to to express the relation between GCF and also LCM of 16 and 24, i.e. GCF × LCM = 16 × 24.