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LCM of 11 and 12

LCM of 11 and 12 is the smallest number among all common multiples of 11 and 12. The first few multiples of 11 and 12 are (11, 22, 33, 44, 55, 66, 77, . . . ) and (12, 24, 36, 48, 60, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 12 - by prime factorization, by division method, and by listing multiples.

1. LCM of 11 and 12
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 11 and 12?

Answer: LCM of 11 and 12 is 132.

LCM of 11 and 12

Explanation:

The LCM of two non-zero integers, x(11) and y(12), is the smallest positive integer m(132) that is divisible by both x(11) and y(12) without any remainder.

Methods to Find LCM of 11 and 12

The methods to find the LCM of 11 and 12 are explained below.

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

LCM of 11 and 12 by Division Method

To calculate the LCM of 11 and 12 by the division method, we will divide the numbers(11, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 12.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 12. Write this prime number(2) on the left of the given numbers(11 and 12), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (11, 12) 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 12 is the product of all prime numbers on the left, i.e. LCM(11, 12) by division method = 2 × 2 × 3 × 11 = 132.

LCM of 11 and 12 by Listing Multiples

LCM of 11 and 12 by Listing Multiples Method

To calculate the LCM of 11 and 12 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 12 (12, 24, 36, 48, 60, . . . . )
  • Step 2: The common multiples from the multiples of 11 and 12 are 132, 264, . . .
  • Step 3: The smallest common multiple of 11 and 12 is 132.

∴ The least common multiple of 11 and 12 = 132.

LCM of 11 and 12 by Prime Factorization

Prime factorization of 11 and 12 is (11) = 111 and (2 × 2 × 3) = 22 × 31 respectively. LCM of 11 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 111 = 132.
Hence, the LCM of 11 and 12 by prime factorization is 132.

☛ Also Check:

LCM of 11 and 12 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 11 and 12.

    Solution:

    The relation between GCF and LCM of 11 and 12 is given as,
    LCM(11, 12) × GCF(11, 12) = Product of 11, 12
    Prime factorization of 11 and 12 is given as, 11 = (11) = 111 and 12 = (2 × 2 × 3) = 22 × 31
    LCM(11, 12) = 132
    GCF(11, 12) = 1
    LHS = LCM(11, 12) × GCF(11, 12) = 132 × 1 = 132
    RHS = Product of 11, 12 = 11 × 12 = 132
    ⇒ LHS = RHS = 132
    Hence, verified.

  2. Example 2: The product of two numbers is 132. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 132
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 132/1
    Therefore, the LCM is 132.
    The probable combination for the given case is LCM(11, 12) = 132.

  3. Example 3: Find the smallest number that is divisible by 11 and 12 exactly.

    Solution:

    The smallest number that is divisible by 11 and 12 exactly is their LCM.
    ⇒ Multiples of 11 and 12:

    • Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, . . . .
    • Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, . . . .

    Therefore, the LCM of 11 and 12 is 132.

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FAQs on LCM of 11 and 12

What is the LCM of 11 and 12?

The LCM of 11 and 12 is 132. To find the LCM (least common multiple) of 11 and 12, we need to find the multiples of 11 and 12 (multiples of 11 = 11, 22, 33, 44 . . . . 132; multiples of 12 = 12, 24, 36, 48 . . . . 132) and choose the smallest multiple that is exactly divisible by 11 and 12, i.e., 132.

What is the Relation Between GCF and LCM of 11, 12?

The following equation can be used to express the relation between GCF and LCM of 11 and 12, i.e. GCF × LCM = 11 × 12.

Which of the following is the LCM of 11 and 12? 20, 18, 36, 132

The value of LCM of 11, 12 is the smallest common multiple of 11 and 12. The number satisfying the given condition is 132.

If the LCM of 12 and 11 is 132, Find its GCF.

LCM(12, 11) × GCF(12, 11) = 12 × 11
Since the LCM of 12 and 11 = 132
⇒ 132 × GCF(12, 11) = 132
Therefore, the greatest common factor = 132/132 = 1.

What are the Methods to Find LCM of 11 and 12?

The commonly used methods to find the LCM of 11 and 12 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method
 
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