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LCM of 11 and 22

LCM of 11 and 22 is the smallest number among all common multiples of 11 and 22. The first few multiples of 11 and 22 are (11, 22, 33, 44, 55, 66, 77, . . . ) and (22, 44, 66, 88, 110, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 22 - by division method, by listing multiples, and by prime factorization.

1. LCM of 11 and 22
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 11 and 22?

Answer: LCM of 11 and 22 is 22.

LCM of 11 and 22

Explanation:

The LCM of two non-zero integers, x(11) and y(22), is the smallest positive integer m(22) that is divisible by both x(11) and y(22) without any remainder.

Methods to Find LCM of 11 and 22

The methods to find the LCM of 11 and 22 are explained below.

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

LCM of 11 and 22 by Division Method

LCM of 11 and 22 by Division Method

To calculate the LCM of 11 and 22 by the division method, we will divide the numbers(11, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 22.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 22. Write this prime number(2) on the left of the given numbers(11 and 22), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (11, 22) 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 11 and 22 is the product of all prime numbers on the left, i.e. LCM(11, 22) by division method = 2 × 11 = 22.

LCM of 11 and 22 by Listing Multiples

To calculate the LCM of 11 and 22 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 11 (11, 22, 33, 44, 55, 66, 77, . . . ) and 22 (22, 44, 66, 88, 110, . . . . )
  • Step 2: The common multiples from the multiples of 11 and 22 are 22, 44, . . .
  • Step 3: The smallest common multiple of 11 and 22 is 22.

∴ The least common multiple of 11 and 22 = 22.

LCM of 11 and 22 by Prime Factorization

Prime factorization of 11 and 22 is (11) = 111 and (2 × 11) = 21 × 111 respectively. LCM of 11 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 111 = 22.
Hence, the LCM of 11 and 22 by prime factorization is 22.

☛ Also Check:

LCM of 11 and 22 Examples

  1. Example 1: The GCD and LCM of two numbers are 11 and 22 respectively. If one number is 11, find the other number.

    Solution:

    Let the other number be m.
    ∵ GCD × LCM = 11 × m
    ⇒ m = (GCD × LCM)/11
    ⇒ m = (11 × 22)/11
    ⇒ m = 22
    Therefore, the other number is 22.

  2. Example 2: Verify the relationship between GCF and LCM of 11 and 22.

    Solution:

    The relation between GCF and LCM of 11 and 22 is given as,
    LCM(11, 22) × GCF(11, 22) = Product of 11, 22
    Prime factorization of 11 and 22 is given as, 11 = (11) = 111 and 22 = (2 × 11) = 21 × 111
    LCM(11, 22) = 22
    GCF(11, 22) = 11
    LHS = LCM(11, 22) × GCF(11, 22) = 22 × 11 = 242
    RHS = Product of 11, 22 = 11 × 22 = 242
    ⇒ LHS = RHS = 242
    Hence, verified.

  3. Example 3: Find the smallest number that is divisible by 11 and 22 exactly.

    Solution:

    The smallest number that is divisible by 11 and 22 exactly is their LCM.
    ⇒ Multiples of 11 and 22:

    • Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, . . . .
    • Multiples of 22 = 22, 44, 66, 88, 110, 132, 154, . . . .

    Therefore, the LCM of 11 and 22 is 22.

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FAQs on LCM of 11 and 22

What is the LCM of 11 and 22?

The LCM of 11 and 22 is 22. To find the least common multiple (LCM) of 11 and 22, we need to find the multiples of 11 and 22 (multiples of 11 = 11, 22, 33, 44; multiples of 22 = 22, 44, 66, 88) and choose the smallest multiple that is exactly divisible by 11 and 22, i.e., 22.

What is the Least Perfect Square Divisible by 11 and 22?

The least number divisible by 11 and 22 = LCM(11, 22)
LCM of 11 and 22 = 2 × 11 [Incomplete pair(s): 2, 11]
⇒ Least perfect square divisible by each 11 and 22 = LCM(11, 22) × 2 × 11 = 484 [Square root of 484 = √484 = ±22]
Therefore, 484 is the required number.

What is the Relation Between GCF and LCM of 11, 22?

The following equation can be used to express the relation between GCF and LCM of 11 and 22, i.e. GCF × LCM = 11 × 22.

If the LCM of 22 and 11 is 22, Find its GCF.

LCM(22, 11) × GCF(22, 11) = 22 × 11
Since the LCM of 22 and 11 = 22
⇒ 22 × GCF(22, 11) = 242
Therefore, the greatest common factor (GCF) = 242/22 = 11.

What are the Methods to Find LCM of 11 and 22?

The commonly used methods to find the LCM of 11 and 22 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples
 
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