LCM of 16 and 40 is the smallest number amongst all typical multiples the 16 and 40. The first couple of multiples of 16 and also 40 are (16, 32, 48, 64, . . . ) and also (40, 80, 120, 160, 200, 240, . . . ) respectively. There room 3 typically used techniques to uncover LCM the 16 and 40 - through listing multiples, by element factorization, and by department method.

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

Answer: LCM that 16 and also 40 is 80.

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Explanation:

The LCM of 2 non-zero integers, x(16) and also y(40), is the smallest optimistic integer m(80) that is divisible through both x(16) and y(40) without any type of remainder.


Let's look in ~ the different methods because that finding the LCM of 16 and also 40.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM that 16 and also 40 by division Method

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To calculate the LCM the 16 and also 40 by the division method, we will certainly divide the numbers(16, 40) by your prime factors (preferably common). The product of these divisors offers the LCM that 16 and 40.

Step 3: continue the procedures until just 1s room left in the last row.

The LCM that 16 and also 40 is the product of every prime numbers on the left, i.e. LCM(16, 40) by department method = 2 × 2 × 2 × 2 × 5 = 80.

LCM of 16 and 40 by prime Factorization

Prime administrate of 16 and 40 is (2 × 2 × 2 × 2) = 24 and (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM of 16 and 40 deserve to be obtained by multiply prime components raised to their respective highest power, i.e. 24 × 51 = 80.Hence, the LCM the 16 and 40 by prime factorization is 80.

LCM that 16 and 40 through Listing Multiples

To calculation the LCM the 16 and 40 by listing out the usual multiples, we have the right to follow the given listed below steps:

Step 1: list a few multiples of 16 (16, 32, 48, 64, . . . ) and also 40 (40, 80, 120, 160, 200, 240, . . . . )Step 2: The typical multiples from the multiples the 16 and 40 space 80, 160, . . .Step 3: The smallest common multiple the 16 and 40 is 80.

∴ The least common multiple of 16 and 40 = 80.

☛ likewise Check:


Example 1: Verify the relationship in between GCF and also LCM that 16 and also 40.

Solution:

The relation in between GCF and also LCM the 16 and 40 is given as,LCM(16, 40) × GCF(16, 40) = Product of 16, 40Prime administer of 16 and 40 is provided as, 16 = (2 × 2 × 2 × 2) = 24 and 40 = (2 × 2 × 2 × 5) = 23 × 51LCM(16, 40) = 80GCF(16, 40) = 8LHS = LCM(16, 40) × GCF(16, 40) = 80 × 8 = 640RHS = Product of 16, 40 = 16 × 40 = 640⇒ LHS = RHS = 640Hence, verified.


Example 3: discover the the smallest number the is divisible by 16 and 40 exactly.

Solution:

The smallest number that is divisible by 16 and also 40 precisely is their LCM.⇒ Multiples that 16 and 40:

Multiples that 16 = 16, 32, 48, 64, 80, . . . .Multiples of 40 = 40, 80, 120, 160, 200, . . . .

Therefore, the LCM the 16 and also 40 is 80.


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FAQs top top LCM the 16 and also 40

What is the LCM of 16 and 40?

The LCM the 16 and 40 is 80. To uncover the least usual multiple the 16 and 40, we require to find the multiples of 16 and 40 (multiples the 16 = 16, 32, 48, 64 . . . . 80; multiples of 40 = 40, 80, 120, 160) and also choose the smallest multiple the is specifically divisible through 16 and also 40, i.e., 80.

If the LCM of 40 and also 16 is 80, discover its GCF.

LCM(40, 16) × GCF(40, 16) = 40 × 16Since the LCM of 40 and also 16 = 80⇒ 80 × GCF(40, 16) = 640Therefore, the greatest typical factor (GCF) = 640/80 = 8.

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

The least number divisible through 16 and 40 = LCM(16, 40)LCM that 16 and also 40 = 2 × 2 × 2 × 2 × 5 ⇒ least perfect square divisible by every 16 and also 40 = LCM(16, 40) × 5 = 400 Therefore, 400 is the required number.

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

The complying with equation can be used to to express the relation between GCF and also LCM that 16 and also 40, i.e. GCF × LCM = 16 × 40.

See more: Question: What Is The Percentage Of 8 Out Of 20 As A Percentage?

How to find the LCM that 16 and also 40 by element Factorization?

To uncover the LCM that 16 and also 40 using prime factorization, us will discover the element factors, (16 = 2 × 2 × 2 × 2) and (40 = 2 × 2 × 2 × 5). LCM the 16 and 40 is the product the prime determinants raised to their respective highest exponent amongst the number 16 and also 40.⇒ LCM the 16, 40 = 24 × 51 = 80.