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LCM of 5 and 11

LCM of 5 and 11 is the smallest number among all common multiples of 5 and 11. The first few multiples of 5 and 11 are (5, 10, 15, 20, 25, 30, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 11 - by division method, by prime factorization, and by listing multiples.

1. LCM of 5 and 11
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 5 and 11?

Answer: LCM of 5 and 11 is 55.

LCM of 5 and 11

Explanation:

The LCM of two non-zero integers, x(5) and y(11), is the smallest positive integer m(55) that is divisible by both x(5) and y(11) without any remainder.

Methods to Find LCM of 5 and 11

The methods to find the LCM of 5 and 11 are explained below.

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

LCM of 5 and 11 by Prime Factorization

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

LCM of 5 and 11 by Listing Multiples

LCM of 5 and 11 by Listing Multiples Method

To calculate the LCM of 5 and 11 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )
  • Step 2: The common multiples from the multiples of 5 and 11 are 55, 110, . . .
  • Step 3: The smallest common multiple of 5 and 11 is 55.

∴ The least common multiple of 5 and 11 = 55.

LCM of 5 and 11 by Division Method

LCM of 5 and 11 by Division Method

To calculate the LCM of 5 and 11 by the division method, we will divide the numbers(5, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 11.

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

☛ Also Check:

LCM of 5 and 11 Examples

  1. Example 1: Find the smallest number that is divisible by 5 and 11 exactly.

    Solution:

    The smallest number that is divisible by 5 and 11 exactly is their LCM.
    ⇒ Multiples of 5 and 11:

    • Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, . . . .
    • Multiples of 11 = 11, 22, 33, 44, 55, 66, . . . .

    Therefore, the LCM of 5 and 11 is 55.

  2. Example 2: The product of two numbers is 55. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 55
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 55/1
    Therefore, the LCM is 55.
    The probable combination for the given case is LCM(5, 11) = 55.

  3. Example 3: The GCD and LCM of two numbers are 1 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 = (1 × 55)/11
    ⇒ m = 5
    Therefore, the other number is 5.

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FAQs on LCM of 5 and 11

What is the LCM of 5 and 11?

The LCM of 5 and 11 is 55. To find the LCM (least common multiple) of 5 and 11, we need to find the multiples of 5 and 11 (multiples of 5 = 5, 10, 15, 20 . . . . 55; multiples of 11 = 11, 22, 33, 44 . . . . 55) and choose the smallest multiple that is exactly divisible by 5 and 11, i.e., 55.

What are the Methods to Find LCM of 5 and 11?

The commonly used methods to find the LCM of 5 and 11 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method

What is the Relation Between GCF and LCM of 5, 11?

The following equation can be used to express the relation between GCF and LCM of 5 and 11, i.e. GCF × LCM = 5 × 11.

If the LCM of 11 and 5 is 55, Find its GCF.

LCM(11, 5) × GCF(11, 5) = 11 × 5
Since the LCM of 11 and 5 = 55
⇒ 55 × GCF(11, 5) = 55
Therefore, the greatest common factor (GCF) = 55/55 = 1.

Which of the following is the LCM of 5 and 11? 15, 24, 12, 55

The value of LCM of 5, 11 is the smallest common multiple of 5 and 11. The number satisfying the given condition is 55.

 
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