LCM the 24, 36, and also 48 is the smallest number amongst all common multiples of 24, 36, and also 48. The first few multiples that 24, 36, and also 48 space (24, 48, 72, 96, 120 . . .), (36, 72, 108, 144, 180 . . .), and (48, 96, 144, 192, 240 . . .) respectively. There room 3 frequently used methods to find LCM that 24, 36, 48 - by element factorization, by department method, and also by listing multiples.

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1.LCM the 24, 36, and 48
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 24, 36, and 48 is 144.

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Explanation:

The LCM of 3 non-zero integers, a(24), b(36), and c(48), is the smallest positive integer m(144) the is divisible by a(24), b(36), and c(48) without any type of remainder.


Let's look at the different methods because that finding the LCM of 24, 36, and also 48.

By prime Factorization MethodBy Listing MultiplesBy division Method

LCM of 24, 36, and also 48 by prime Factorization

Prime administer of 24, 36, and 48 is (2 × 2 × 2 × 3) = 23 × 31, (2 × 2 × 3 × 3) = 22 × 32, and (2 × 2 × 2 × 2 × 3) = 24 × 31 respectively. LCM that 24, 36, and 48 have the right to be derived by multiplying prime components raised to your respective greatest power, i.e. 24 × 32 = 144.Hence, the LCM that 24, 36, and 48 by element factorization is 144.

LCM of 24, 36, and 48 through Listing Multiples

To calculation the LCM that 24, 36, 48 by listing the end the typical multiples, we have the right to follow the given listed below steps:

Step 1: list a couple of multiples of 24 (24, 48, 72, 96, 120 . . .), 36 (36, 72, 108, 144, 180 . . .), and also 48 (48, 96, 144, 192, 240 . . .).Step 2: The common multiples indigenous the multiples of 24, 36, and also 48 are 144, 288, . . .Step 3: The smallest usual multiple of 24, 36, and 48 is 144.

∴ The least common multiple the 24, 36, and 48 = 144.

LCM the 24, 36, and also 48 by department Method

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To calculation the LCM that 24, 36, and 48 by the division method, we will divide the numbers(24, 36, 48) by your prime determinants (preferably common). The product of these divisors gives the LCM the 24, 36, and 48.

Step 2: If any type of of the offered numbers (24, 36, 48) is a many of 2, divide it through 2 and also write the quotient listed below it. Lug down any number the is no divisible by the element number.Step 3: continue the measures until only 1s space left in the last row.

The LCM the 24, 36, and also 48 is the product of all prime number on the left, i.e. LCM(24, 36, 48) by department method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

☛ also Check:


Example 1: Verify the relationship between the GCD and also LCM of 24, 36, and also 48.

Solution:

The relation in between GCD and LCM that 24, 36, and also 48 is given as,LCM(24, 36, 48) = <(24 × 36 × 48) × GCD(24, 36, 48)>/⇒ element factorization that 24, 36 and also 48:

24 = 23 × 3136 = 22 × 3248 = 24 × 31

∴ GCD the (24, 36), (36, 48), (24, 48) and (24, 36, 48) = 12, 12, 24 and 12 respectively.Now, LHS = LCM(24, 36, 48) = 144.And, RHS = <(24 × 36 × 48) × GCD(24, 36, 48)>/ = <(41472) × 12>/<12 × 12 × 24> = 144LHS = RHS = 144.Hence verified.


Example 2: find the smallest number that is divisible through 24, 36, 48 exactly.

Solution:

The the smallest number that is divisible through 24, 36, and also 48 precisely is their LCM.⇒ Multiples that 24, 36, and 48:

Multiples that 24 = 24, 48, 72, 96, 120, 144, . . . .Multiples that 36 = 36, 72, 108, 144, 180, . . . .Multiples that 48 = 48, 96, 144, 192, 240, . . . .

Therefore, the LCM of 24, 36, and also 48 is 144.


Example 3: calculate the LCM that 24, 36, and also 48 utilizing the GCD the the given numbers.

Solution:

Prime administrate of 24, 36, 48:

24 = 23 × 3136 = 22 × 3248 = 24 × 31

Therefore, GCD(24, 36) = 12, GCD(36, 48) = 12, GCD(24, 48) = 24, GCD(24, 36, 48) = 12We know,LCM(24, 36, 48) = <(24 × 36 × 48) × GCD(24, 36, 48)>/LCM(24, 36, 48) = (41472 × 12)/(12 × 12 × 24) = 144⇒LCM(24, 36, 48) = 144


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FAQs top top LCM the 24, 36, and also 48

What is the LCM that 24, 36, and also 48?

The LCM that 24, 36, and also 48 is 144. To uncover the least typical multiple (LCM) the 24, 36, and 48, we need to uncover the multiples of 24, 36, and 48 (multiples of 24 = 24, 48, 72, 96, 144 . . . .; multiples that 36 = 36, 72, 108, 144 . . . .; multiples of 48 = 48, 96, 144, 192 . . . .) and choose the smallest multiple the is exactly divisible by 24, 36, and 48, i.e., 144.

What room the methods to uncover LCM that 24, 36, 48?

The frequently used methods to uncover the LCM of 24, 36, 48 are:

Division MethodListing MultiplesPrime factorization Method

Which that the adhering to is the LCM of 24, 36, and 48? 120, 2, 30, 144

The worth of LCM the 24, 36, 48 is the smallest common multiple of 24, 36, and also 48. The number to solve the given condition is 144.

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What is the Relation in between GCF and also LCM of 24, 36, 48?

The complying with equation have the right to be offered to refer the relation between GCF and LCM that 24, 36, 48, i.e. LCM(24, 36, 48) = <(24 × 36 × 48) × GCF(24, 36, 48)>/.