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LCM of 21 and 27

LCM of 21 and 27 is the smallest number among all common multiples of 21 and 27. The first few multiples of 21 and 27 are (21, 42, 63, 84, 105, 126, 147, . . . ) and (27, 54, 81, 108, 135, 162, 189, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 27 - by listing multiples, by prime factorization, and by division method.

1. LCM of 21 and 27
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 21 and 27?

Answer: LCM of 21 and 27 is 189.

LCM of 21 and 27

Explanation:

The LCM of two non-zero integers, x(21) and y(27), is the smallest positive integer m(189) that is divisible by both x(21) and y(27) without any remainder.

Methods to Find LCM of 21 and 27

The methods to find the LCM of 21 and 27 are explained below.

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

LCM of 21 and 27 by Prime Factorization

Prime factorization of 21 and 27 is (3 × 7) = 31 × 71 and (3 × 3 × 3) = 33 respectively. LCM of 21 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 33 × 71 = 189.
Hence, the LCM of 21 and 27 by prime factorization is 189.

LCM of 21 and 27 by Division Method

LCM of 21 and 27 by Division Method

To calculate the LCM of 21 and 27 by the division method, we will divide the numbers(21, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 27.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 27. Write this prime number(3) on the left of the given numbers(21 and 27), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (21, 27) is a multiple of 3, divide it by 3 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 21 and 27 is the product of all prime numbers on the left, i.e. LCM(21, 27) by division method = 3 × 3 × 3 × 7 = 189.

LCM of 21 and 27 by Listing Multiples

LCM of 21 and 27 by Listing Multiples Method

To calculate the LCM of 21 and 27 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 21 (21, 42, 63, 84, 105, 126, 147, . . . ) and 27 (27, 54, 81, 108, 135, 162, 189, . . . . )
  • Step 2: The common multiples from the multiples of 21 and 27 are 189, 378, . . .
  • Step 3: The smallest common multiple of 21 and 27 is 189.

∴ The least common multiple of 21 and 27 = 189.

☛ Also Check:

LCM of 21 and 27 Examples

  1. Example 1: The GCD and LCM of two numbers are 3 and 189 respectively. If one number is 27, find the other number.

    Solution:

    Let the other number be z.
    ∵ GCD × LCM = 27 × z
    ⇒ z = (GCD × LCM)/27
    ⇒ z = (3 × 189)/27
    ⇒ z = 21
    Therefore, the other number is 21.

  2. Example 2: Find the smallest number that is divisible by 21 and 27 exactly.

    Solution:

    The smallest number that is divisible by 21 and 27 exactly is their LCM.
    ⇒ Multiples of 21 and 27:

    • Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, . . . .
    • Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, . . . .

    Therefore, the LCM of 21 and 27 is 189.

  3. Example 3: Verify the relationship between GCF and LCM of 21 and 27.

    Solution:

    The relation between GCF and LCM of 21 and 27 is given as,
    LCM(21, 27) × GCF(21, 27) = Product of 21, 27
    Prime factorization of 21 and 27 is given as, 21 = (3 × 7) = 31 × 71 and 27 = (3 × 3 × 3) = 33
    LCM(21, 27) = 189
    GCF(21, 27) = 3
    LHS = LCM(21, 27) × GCF(21, 27) = 189 × 3 = 567
    RHS = Product of 21, 27 = 21 × 27 = 567
    ⇒ LHS = RHS = 567
    Hence, verified.

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FAQs on LCM of 21 and 27

What is the LCM of 21 and 27?

The LCM of 21 and 27 is 189. To find the LCM (least common multiple) of 21 and 27, we need to find the multiples of 21 and 27 (multiples of 21 = 21, 42, 63, 84 . . . . 189; multiples of 27 = 27, 54, 81, 108 . . . . 189) and choose the smallest multiple that is exactly divisible by 21 and 27, i.e., 189.

If the LCM of 27 and 21 is 189, Find its GCF.

LCM(27, 21) × GCF(27, 21) = 27 × 21
Since the LCM of 27 and 21 = 189
⇒ 189 × GCF(27, 21) = 567
Therefore, the GCF = 567/189 = 3.

What is the Relation Between GCF and LCM of 21, 27?

The following equation can be used to express the relation between GCF and LCM of 21 and 27, i.e. GCF × LCM = 21 × 27.

What are the Methods to Find LCM of 21 and 27?

The commonly used methods to find the LCM of 21 and 27 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method

Which of the following is the LCM of 21 and 27? 30, 24, 189, 32

The value of LCM of 21, 27 is the smallest common multiple of 21 and 27. The number satisfying the given condition is 189.

 
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