A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

LCM of 3, 5, and 11

LCM of 3, 5, and 11 is the smallest number among all common multiples of 3, 5, and 11. The first few multiples of 3, 5, and 11 are (3, 6, 9, 12, 15 . . .), (5, 10, 15, 20, 25 . . .), and (11, 22, 33, 44, 55 . . .) respectively. There are 3 commonly used methods to find LCM of 3, 5, 11 - by division method, by prime factorization, and by listing multiples.

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

What is the LCM of 3, 5, and 11?

Answer: LCM of 3, 5, and 11 is 165.

LCM of 3, 5, and 11

Explanation:

The LCM of three non-zero integers, a(3), b(5), and c(11), is the smallest positive integer m(165) that is divisible by a(3), b(5), and c(11) without any remainder.

Methods to Find LCM of 3, 5, and 11

The methods to find the LCM of 3, 5, and 11 are explained below.

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

LCM of 3, 5, and 11 by Division Method

LCM of 3, 5, and 11 by Division Method

To calculate the LCM of 3, 5, and 11 by the division method, we will divide the numbers(3, 5, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 3, 5, and 11.

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

LCM of 3, 5, and 11 by Listing Multiples

LCM of 3, 5, and 11 by Listing Multiples Method

To calculate the LCM of 3, 5, 11 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 3 (3, 6, 9, 12, 15 . . .), 5 (5, 10, 15, 20, 25 . . .), and 11 (11, 22, 33, 44, 55 . . .).
  • Step 2: The common multiples from the multiples of 3, 5, and 11 are 165, 330, . . .
  • Step 3: The smallest common multiple of 3, 5, and 11 is 165.

∴ The least common multiple of 3, 5, and 11 = 165.

LCM of 3, 5, and 11 by Prime Factorization

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

☛ Also Check:

LCM of 3, 5, and 11 Examples

  1. Example 1: Calculate the LCM of 3, 5, and 11 using the GCD of the given numbers.

    Solution:

    Prime factorization of 3, 5, 11:

    • 3 = 31
    • 5 = 51
    • 11 = 111

    Therefore, GCD(3, 5) = 1, GCD(5, 11) = 1, GCD(3, 11) = 1, GCD(3, 5, 11) = 1
    We know,
    LCM(3, 5, 11) = [(3 × 5 × 11) × GCD(3, 5, 11)]/[GCD(3, 5) × GCD(5, 11) × GCD(3, 11)]
    LCM(3, 5, 11) = (165 × 1)/(1 × 1 × 1) = 165
    ⇒LCM(3, 5, 11) = 165

  2. Example 2: Find the smallest number that is divisible by 3, 5, 11 exactly.

    Solution:

    The value of LCM(3, 5, 11) will be the smallest number that is exactly divisible by 3, 5, and 11.
    ⇒ Multiples of 3, 5, and 11:

    • Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 153, 156, 159, 162, 165, . . . .
    • Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 155, 160, 165, . . . .
    • Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, . . . ., 121, 132, 143, 154, 165, . . . .

    Therefore, the LCM of 3, 5, and 11 is 165.

  3. Example 3: Verify the relationship between the GCD and LCM of 3, 5, and 11.

    Solution:

    The relation between GCD and LCM of 3, 5, and 11 is given as,
    LCM(3, 5, 11) = [(3 × 5 × 11) × GCD(3, 5, 11)]/[GCD(3, 5) × GCD(5, 11) × GCD(3, 11)]
    ⇒ Prime factorization of 3, 5 and 11:

    • 3 = 31
    • 5 = 51
    • 11 = 111

    ∴ GCD of (3, 5), (5, 11), (3, 11) and (3, 5, 11) = 1, 1, 1 and 1 respectively.
    Now, LHS = LCM(3, 5, 11) = 165.
    And, RHS = [(3 × 5 × 11) × GCD(3, 5, 11)]/[GCD(3, 5) × GCD(5, 11) × GCD(3, 11)] = [(165) × 1]/[1 × 1 × 1] = 165
    LHS = RHS = 165.
    Hence verified.

Show Solution >

go to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

FAQs on LCM of 3, 5, and 11

What is the LCM of 3, 5, and 11?

The LCM of 3, 5, and 11 is 165. To find the LCM of 3, 5, and 11, we need to find the multiples of 3, 5, and 11 (multiples of 3 = 3, 6, 9, 12 . . . . 165 . . . . ; multiples of 5 = 5, 10, 15, 20 . . . . 165 . . . . ; multiples of 11 = 11, 22, 33, 44 . . . . 165 . . . . ) and choose the smallest multiple that is exactly divisible by 3, 5, and 11, i.e., 165.

Which of the following is the LCM of 3, 5, and 11? 165, 35, 30, 45

The value of LCM of 3, 5, 11 is the smallest common multiple of 3, 5, and 11. The number satisfying the given condition is 165.

How to Find the LCM of 3, 5, and 11 by Prime Factorization?

To find the LCM of 3, 5, and 11 using prime factorization, we will find the prime factors, (3 = 31), (5 = 51), and (11 = 111). LCM of 3, 5, and 11 is the product of prime factors raised to their respective highest exponent among the numbers 3, 5, and 11.
⇒ LCM of 3, 5, 11 = 31 × 51 × 111 = 165.

What are the Methods to Find LCM of 3, 5, 11?

The commonly used methods to find the LCM of 3, 5, 11 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method
 
Download FREE Study Materials
LCM and GCF
Math worksheets and
visual curriculum