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LCM of 11 and 15

LCM of 11 and 15 is the smallest number among all common multiples of 11 and 15. The first few multiples of 11 and 15 are (11, 22, 33, 44, 55, 66, 77, . . . ) and (15, 30, 45, 60, 75, 90, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 15 - by prime factorization, by listing multiples, and by division method.

1. LCM of 11 and 15
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 11 and 15?

Answer: LCM of 11 and 15 is 165.

LCM of 11 and 15

Explanation:

The LCM of two non-zero integers, x(11) and y(15), is the smallest positive integer m(165) that is divisible by both x(11) and y(15) without any remainder.

Methods to Find LCM of 11 and 15

The methods to find the LCM of 11 and 15 are explained below.

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

LCM of 11 and 15 by Prime Factorization

Prime factorization of 11 and 15 is (11) = 111 and (3 × 5) = 31 × 51 respectively. LCM of 11 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 31 × 51 × 111 = 165.
Hence, the LCM of 11 and 15 by prime factorization is 165.

LCM of 11 and 15 by Listing Multiples

LCM of 11 and 15 by Listing Multiples Method

To calculate the LCM of 11 and 15 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 15 (15, 30, 45, 60, 75, 90, 105, . . . . )
  • Step 2: The common multiples from the multiples of 11 and 15 are 165, 330, . . .
  • Step 3: The smallest common multiple of 11 and 15 is 165.

∴ The least common multiple of 11 and 15 = 165.

LCM of 11 and 15 by Division Method

LCM of 11 and 15 by Division Method

To calculate the LCM of 11 and 15 by the division method, we will divide the numbers(11, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 15.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 15. Write this prime number(3) on the left of the given numbers(11 and 15), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (11, 15) 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 11 and 15 is the product of all prime numbers on the left, i.e. LCM(11, 15) by division method = 3 × 5 × 11 = 165.

☛ Also Check:

LCM of 11 and 15 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 11 and 15.

    Solution:

    The relation between GCF and LCM of 11 and 15 is given as,
    LCM(11, 15) × GCF(11, 15) = Product of 11, 15
    Prime factorization of 11 and 15 is given as, 11 = (11) = 111 and 15 = (3 × 5) = 31 × 51
    LCM(11, 15) = 165
    GCF(11, 15) = 1
    LHS = LCM(11, 15) × GCF(11, 15) = 165 × 1 = 165
    RHS = Product of 11, 15 = 11 × 15 = 165
    ⇒ LHS = RHS = 165
    Hence, verified.

  2. Example 2: The GCD and LCM of two numbers are 1 and 165 respectively. If one number is 15, find the other number.

    Solution:

    Let the other number be p.
    ∵ GCD × LCM = 15 × p
    ⇒ p = (GCD × LCM)/15
    ⇒ p = (1 × 165)/15
    ⇒ p = 11
    Therefore, the other number is 11.

  3. Example 3: Find the smallest number that is divisible by 11 and 15 exactly.

    Solution:

    The smallest number that is divisible by 11 and 15 exactly is their LCM.
    ⇒ Multiples of 11 and 15:

    • Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, . . . .
    • Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, . . . .

    Therefore, the LCM of 11 and 15 is 165.

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FAQs on LCM of 11 and 15

What is the LCM of 11 and 15?

The LCM of 11 and 15 is 165. To find the LCM of 11 and 15, we need to find the multiples of 11 and 15 (multiples of 11 = 11, 22, 33, 44 . . . . 165; multiples of 15 = 15, 30, 45, 60 . . . . 165) and choose the smallest multiple that is exactly divisible by 11 and 15, i.e., 165.

Which of the following is the LCM of 11 and 15? 40, 25, 165, 50

The value of LCM of 11, 15 is the smallest common multiple of 11 and 15. The number satisfying the given condition is 165.

If the LCM of 15 and 11 is 165, Find its GCF.

LCM(15, 11) × GCF(15, 11) = 15 × 11
Since the LCM of 15 and 11 = 165
⇒ 165 × GCF(15, 11) = 165
Therefore, the GCF (greatest common factor) = 165/165 = 1.

What is the Relation Between GCF and LCM of 11, 15?

The following equation can be used to express the relation between GCF and LCM of 11 and 15, i.e. GCF × LCM = 11 × 15.

What are the Methods to Find LCM of 11 and 15?

The commonly used methods to find the LCM of 11 and 15 are:

  • Listing Multiples
  • Division Method
  • Prime Factorization Method
 
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