LCM of 48 and 72 is the the smallest number amongst all common multiples the 48 and 72. The first few multiples of 48 and also 72 room (48, 96, 144, 192, . . . ) and (72, 144, 216, 288, 360, 432, 504, . . . ) respectively. There room 3 generally used techniques to discover LCM the 48 and 72 - by element factorization, by department method, and also by listing multiples.

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1.LCM that 48 and 72
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 48 and also 72 is 144.

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Explanation:

The LCM of 2 non-zero integers, x(48) and also y(72), is the smallest positive integer m(144) the is divisible through both x(48) and also y(72) without any remainder.


The approaches to discover the LCM of 48 and also 72 are described below.

By element Factorization MethodBy department MethodBy Listing Multiples

LCM of 48 and 72 by element Factorization

Prime administrate of 48 and also 72 is (2 × 2 × 2 × 2 × 3) = 24 × 31 and (2 × 2 × 2 × 3 × 3) = 23 × 32 respectively. LCM that 48 and 72 deserve to be acquired by multiplying prime factors raised to their respective highest power, i.e. 24 × 32 = 144.Hence, the LCM of 48 and also 72 by prime factorization is 144.

LCM the 48 and 72 by division Method

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To calculate the LCM of 48 and 72 through the division method, we will certainly divide the numbers(48, 72) by your prime determinants (preferably common). The product of these divisors provides the LCM that 48 and 72.

Step 3: proceed the actions until just 1s space left in the last row.

The LCM that 48 and also 72 is the product of all prime number on the left, i.e. LCM(48, 72) by department method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

LCM that 48 and 72 through Listing Multiples

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To calculation the LCM the 48 and also 72 by listing the end the common multiples, we have the right to follow the given listed below steps:

Step 1: perform a few multiples the 48 (48, 96, 144, 192, . . . ) and 72 (72, 144, 216, 288, 360, 432, 504, . . . . )Step 2: The usual multiples indigenous the multiples the 48 and 72 space 144, 288, . . .Step 3: The smallest usual multiple of 48 and also 72 is 144.

∴ The least common multiple the 48 and 72 = 144.

☛ also Check:


Example 2: Verify the relationship in between GCF and LCM the 48 and 72.

Solution:

The relation in between GCF and LCM of 48 and also 72 is offered as,LCM(48, 72) × GCF(48, 72) = Product of 48, 72Prime administrate of 48 and also 72 is provided as, 48 = (2 × 2 × 2 × 2 × 3) = 24 × 31 and 72 = (2 × 2 × 2 × 3 × 3) = 23 × 32LCM(48, 72) = 144GCF(48, 72) = 24LHS = LCM(48, 72) × GCF(48, 72) = 144 × 24 = 3456RHS = Product of 48, 72 = 48 × 72 = 3456⇒ LHS = RHS = 3456Hence, verified.


Example 3: The product of two numbers is 3456. If your GCD is 24, what is your LCM?

Solution:

Given: GCD = 24product of numbers = 3456∵ LCM × GCD = product that numbers⇒ LCM = Product/GCD = 3456/24Therefore, the LCM is 144.The probable mix for the given case is LCM(48, 72) = 144.


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FAQs top top LCM that 48 and also 72

What is the LCM the 48 and 72?

The LCM the 48 and also 72 is 144. To uncover the LCM (least common multiple) of 48 and 72, we require to discover the multiples that 48 and 72 (multiples that 48 = 48, 96, 144, 192; multiples of 72 = 72, 144, 216, 288) and choose the the smallest multiple the is specifically divisible by 48 and 72, i.e., 144.

Which that the adhering to is the LCM of 48 and also 72? 11, 50, 144, 5

The value of LCM that 48, 72 is the smallest typical multiple that 48 and 72. The number satisfying the given problem is 144.

What is the Relation between GCF and LCM that 48, 72?

The following equation have the right to be used to to express the relation in between GCF and also LCM of 48 and also 72, i.e. GCF × LCM = 48 × 72.

What are the techniques to uncover LCM that 48 and also 72?

The typically used methods to uncover the LCM the 48 and 72 are:

Prime administer MethodDivision MethodListing Multiples

If the LCM of 72 and 48 is 144, discover its GCF.

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LCM(72, 48) × GCF(72, 48) = 72 × 48Since the LCM of 72 and 48 = 144⇒ 144 × GCF(72, 48) = 3456Therefore, the GCF (greatest usual factor) = 3456/144 = 24.