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LCM of 13 and 39

LCM of 13 and 39 is the smallest number among all common multiples of 13 and 39. The first few multiples of 13 and 39 are (13, 26, 39, 52, 65, . . . ) and (39, 78, 117, 156, 195, 234, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 39 - by prime factorization, by division method, and by listing multiples.

1. LCM of 13 and 39
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 13 and 39?

Answer: LCM of 13 and 39 is 39.

LCM of 13 and 39

Explanation:

The LCM of two non-zero integers, x(13) and y(39), is the smallest positive integer m(39) that is divisible by both x(13) and y(39) without any remainder.

Methods to Find LCM of 13 and 39

The methods to find the LCM of 13 and 39 are explained below.

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

LCM of 13 and 39 by Prime Factorization

Prime factorization of 13 and 39 is (13) = 131 and (3 × 13) = 31 × 131 respectively. LCM of 13 and 39 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 31 × 131 = 39.
Hence, the LCM of 13 and 39 by prime factorization is 39.

LCM of 13 and 39 by Listing Multiples

To calculate the LCM of 13 and 39 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 13 (13, 26, 39, 52, 65, . . . ) and 39 (39, 78, 117, 156, 195, 234, . . . . )
  • Step 2: The common multiples from the multiples of 13 and 39 are 39, 78, . . .
  • Step 3: The smallest common multiple of 13 and 39 is 39.

∴ The least common multiple of 13 and 39 = 39.

LCM of 13 and 39 by Division Method

LCM of 13 and 39 by Division Method

To calculate the LCM of 13 and 39 by the division method, we will divide the numbers(13, 39) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 39.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 39. Write this prime number(3) on the left of the given numbers(13 and 39), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (13, 39) 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 13 and 39 is the product of all prime numbers on the left, i.e. LCM(13, 39) by division method = 3 × 13 = 39.

☛ Also Check:

LCM of 13 and 39 Examples

  1. Example 1: The GCD and LCM of two numbers are 13 and 39 respectively. If one number is 39, find the other number.

    Solution:

    Let the other number be b.
    ∵ GCD × LCM = 39 × b
    ⇒ b = (GCD × LCM)/39
    ⇒ b = (13 × 39)/39
    ⇒ b = 13
    Therefore, the other number is 13.

  2. Example 2: The product of two numbers is 507. If their GCD is 13, what is their LCM?

    Solution:

    Given: GCD = 13
    product of numbers = 507
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 507/13
    Therefore, the LCM is 39.
    The probable combination for the given case is LCM(13, 39) = 39.

  3. Example 3: Verify the relationship between GCF and LCM of 13 and 39.

    Solution:

    The relation between GCF and LCM of 13 and 39 is given as,
    LCM(13, 39) × GCF(13, 39) = Product of 13, 39
    Prime factorization of 13 and 39 is given as, 13 = (13) = 131 and 39 = (3 × 13) = 31 × 131
    LCM(13, 39) = 39
    GCF(13, 39) = 13
    LHS = LCM(13, 39) × GCF(13, 39) = 39 × 13 = 507
    RHS = Product of 13, 39 = 13 × 39 = 507
    ⇒ LHS = RHS = 507
    Hence, verified.

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FAQs on LCM of 13 and 39

What is the LCM of 13 and 39?

The LCM of 13 and 39 is 39. To find the least common multiple (LCM) of 13 and 39, we need to find the multiples of 13 and 39 (multiples of 13 = 13, 26, 39, 52; multiples of 39 = 39, 78, 117, 156) and choose the smallest multiple that is exactly divisible by 13 and 39, i.e., 39.

What is the Relation Between GCF and LCM of 13, 39?

The following equation can be used to express the relation between GCF and LCM of 13 and 39, i.e. GCF × LCM = 13 × 39.

Which of the following is the LCM of 13 and 39? 10, 39, 35, 12

The value of LCM of 13, 39 is the smallest common multiple of 13 and 39. The number satisfying the given condition is 39.

If the LCM of 39 and 13 is 39, Find its GCF.

LCM(39, 13) × GCF(39, 13) = 39 × 13
Since the LCM of 39 and 13 = 39
⇒ 39 × GCF(39, 13) = 507
Therefore, the greatest common factor = 507/39 = 13.

What are the Methods to Find LCM of 13 and 39?

The commonly used methods to find the LCM of 13 and 39 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method
 
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