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LCM of 27 and 48

LCM of 27 and 48 is the smallest number among all common multiples of 27 and 48. The first few multiples of 27 and 48 are (27, 54, 81, 108, 135, 162, 189, . . . ) and (48, 96, 144, 192, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 27 and 48 - by division method, by listing multiples, and by prime factorization.

1. LCM of 27 and 48
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 27 and 48?

Answer: LCM of 27 and 48 is 432.

LCM of 27 and 48

Explanation:

The LCM of two non-zero integers, x(27) and y(48), is the smallest positive integer m(432) that is divisible by both x(27) and y(48) without any remainder.

Methods to Find LCM of 27 and 48

The methods to find the LCM of 27 and 48 are explained below.

  • By Prime Factorization Method
  • By Listing Multiples
  • By Division Method

LCM of 27 and 48 by Prime Factorization

Prime factorization of 27 and 48 is (3 × 3 × 3) = 33 and (2 × 2 × 2 × 2 × 3) = 24 × 31 respectively. LCM of 27 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 33 = 432.
Hence, the LCM of 27 and 48 by prime factorization is 432.

LCM of 27 and 48 by Listing Multiples

To calculate the LCM of 27 and 48 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 27 (27, 54, 81, 108, 135, 162, 189, . . . ) and 48 (48, 96, 144, 192, 240, . . . . )
  • Step 2: The common multiples from the multiples of 27 and 48 are 432, 864, . . .
  • Step 3: The smallest common multiple of 27 and 48 is 432.

∴ The least common multiple of 27 and 48 = 432.

LCM of 27 and 48 by Division Method

LCM of 27 and 48 by Division Method

To calculate the LCM of 27 and 48 by the division method, we will divide the numbers(27, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 27 and 48.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 27 and 48. Write this prime number(2) on the left of the given numbers(27 and 48), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (27, 48) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
  • Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 27 and 48 is the product of all prime numbers on the left, i.e. LCM(27, 48) by division method = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432.

☛ Also Check:

LCM of 27 and 48 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 27 and 48.

    Solution:

    The relation between GCF and LCM of 27 and 48 is given as,
    LCM(27, 48) × GCF(27, 48) = Product of 27, 48
    Prime factorization of 27 and 48 is given as, 27 = (3 × 3 × 3) = 33 and 48 = (2 × 2 × 2 × 2 × 3) = 24 × 31
    LCM(27, 48) = 432
    GCF(27, 48) = 3
    LHS = LCM(27, 48) × GCF(27, 48) = 432 × 3 = 1296
    RHS = Product of 27, 48 = 27 × 48 = 1296
    ⇒ LHS = RHS = 1296
    Hence, verified.

  2. Example 2: Find the smallest number that is divisible by 27 and 48 exactly.

    Solution:

    The value of LCM(27, 48) will be the smallest number that is exactly divisible by 27 and 48.
    ⇒ Multiples of 27 and 48:

    • Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, . . . ., 324, 351, 378, 405, 432, . . . .
    • Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, . . . ., 288, 336, 384, 432, . . . .

    Therefore, the LCM of 27 and 48 is 432.

  3. Example 3: The product of two numbers is 1296. If their GCD is 3, what is their LCM?

    Solution:

    Given: GCD = 3
    product of numbers = 1296
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 1296/3
    Therefore, the LCM is 432.
    The probable combination for the given case is LCM(27, 48) = 432.

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FAQs on LCM of 27 and 48

What is the LCM of 27 and 48?

The LCM of 27 and 48 is 432. To find the LCM (least common multiple) of 27 and 48, we need to find the multiples of 27 and 48 (multiples of 27 = 27, 54, 81, 108 . . . . 432; multiples of 48 = 48, 96, 144, 192 . . . . 432) and choose the smallest multiple that is exactly divisible by 27 and 48, i.e., 432.

What is the Least Perfect Square Divisible by 27 and 48?

The least number divisible by 27 and 48 = LCM(27, 48)
LCM of 27 and 48 = 2 × 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 27 and 48 = LCM(27, 48) × 3 = 1296 [Square root of 1296 = √1296 = ±36]
Therefore, 1296 is the required number.

What are the Methods to Find LCM of 27 and 48?

The commonly used methods to find the LCM of 27 and 48 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

Which of the following is the LCM of 27 and 48? 3, 10, 36, 432

The value of LCM of 27, 48 is the smallest common multiple of 27 and 48. The number satisfying the given condition is 432.

If the LCM of 48 and 27 is 432, Find its GCF.

LCM(48, 27) × GCF(48, 27) = 48 × 27
Since the LCM of 48 and 27 = 432
⇒ 432 × GCF(48, 27) = 1296
Therefore, the greatest common factor (GCF) = 1296/432 = 3.

 
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