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LCM of 11 and 55

LCM of 11 and 55 is the smallest number among all common multiples of 11 and 55. The first few multiples of 11 and 55 are (11, 22, 33, 44, 55, 66, . . . ) and (55, 110, 165, 220, 275, 330, 385, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 55 - by division method, by listing multiples, and by prime factorization.

1. LCM of 11 and 55
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 11 and 55?

Answer: LCM of 11 and 55 is 55.

LCM of 11 and 55

Explanation:

The LCM of two non-zero integers, x(11) and y(55), is the smallest positive integer m(55) that is divisible by both x(11) and y(55) without any remainder.

Methods to Find LCM of 11 and 55

The methods to find the LCM of 11 and 55 are explained below.

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

LCM of 11 and 55 by Division Method

LCM of 11 and 55 by Division Method

To calculate the LCM of 11 and 55 by the division method, we will divide the numbers(11, 55) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 55.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 55. Write this prime number(5) on the left of the given numbers(11 and 55), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (11, 55) is a multiple of 5, divide it by 5 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 55 is the product of all prime numbers on the left, i.e. LCM(11, 55) by division method = 5 × 11 = 55.

LCM of 11 and 55 by Prime Factorization

Prime factorization of 11 and 55 is (11) = 111 and (5 × 11) = 51 × 111 respectively. LCM of 11 and 55 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 51 × 111 = 55.
Hence, the LCM of 11 and 55 by prime factorization is 55.

LCM of 11 and 55 by Listing Multiples

To calculate the LCM of 11 and 55 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, . . . ) and 55 (55, 110, 165, 220, 275, 330, 385, . . . . )
  • Step 2: The common multiples from the multiples of 11 and 55 are 55, 110, . . .
  • Step 3: The smallest common multiple of 11 and 55 is 55.

∴ The least common multiple of 11 and 55 = 55.

☛ Also Check:

LCM of 11 and 55 Examples

  1. Example 1: Find the smallest number that is divisible by 11 and 55 exactly.

    Solution:

    The smallest number that is divisible by 11 and 55 exactly is their LCM.
    ⇒ Multiples of 11 and 55:

    • Multiples of 11 = 11, 22, 33, 44, 55, . . . .
    • Multiples of 55 = 55, 110, 165, 220, 275, . . . .

    Therefore, the LCM of 11 and 55 is 55.

  2. Example 2: Verify the relationship between GCF and LCM of 11 and 55.

    Solution:

    The relation between GCF and LCM of 11 and 55 is given as,
    LCM(11, 55) × GCF(11, 55) = Product of 11, 55
    Prime factorization of 11 and 55 is given as, 11 = (11) = 111 and 55 = (5 × 11) = 51 × 111
    LCM(11, 55) = 55
    GCF(11, 55) = 11
    LHS = LCM(11, 55) × GCF(11, 55) = 55 × 11 = 605
    RHS = Product of 11, 55 = 11 × 55 = 605
    ⇒ LHS = RHS = 605
    Hence, verified.

  3. Example 3: The GCD and LCM of two numbers are 11 and 55 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 × 55)/11
    ⇒ m = 55
    Therefore, the other number is 55.

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FAQs on LCM of 11 and 55

What is the LCM of 11 and 55?

The LCM of 11 and 55 is 55. To find the least common multiple of 11 and 55, we need to find the multiples of 11 and 55 (multiples of 11 = 11, 22, 33, 44 . . . . 55; multiples of 55 = 55, 110, 165, 220) and choose the smallest multiple that is exactly divisible by 11 and 55, i.e., 55.

What is the Relation Between GCF and LCM of 11, 55?

The following equation can be used to express the relation between GCF and LCM of 11 and 55, i.e. GCF × LCM = 11 × 55.

What are the Methods to Find LCM of 11 and 55?

The commonly used methods to find the LCM of 11 and 55 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method

If the LCM of 55 and 11 is 55, Find its GCF.

LCM(55, 11) × GCF(55, 11) = 55 × 11
Since the LCM of 55 and 11 = 55
⇒ 55 × GCF(55, 11) = 605
Therefore, the greatest common factor = 605/55 = 11.

Which of the following is the LCM of 11 and 55? 12, 55, 45, 10

The value of LCM of 11, 55 is the smallest common multiple of 11 and 55. The number satisfying the given condition is 55.

 
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