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LCM of 12 and 13

LCM of 12 and 13 is the smallest number among all common multiples of 12 and 13. The first few multiples of 12 and 13 are (12, 24, 36, 48, 60, 72, . . . ) and (13, 26, 39, 52, 65, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 13 - by division method, by prime factorization, and by listing multiples.

1. LCM of 12 and 13
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 12 and 13?

Answer: LCM of 12 and 13 is 156.

LCM of 12 and 13

Explanation:

The LCM of two non-zero integers, x(12) and y(13), is the smallest positive integer m(156) that is divisible by both x(12) and y(13) without any remainder.

Methods to Find LCM of 12 and 13

Let's look at the different methods for finding the LCM of 12 and 13.

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

LCM of 12 and 13 by Division Method

LCM of 12 and 13 by Division Method

To calculate the LCM of 12 and 13 by the division method, we will divide the numbers(12, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 13.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 13. Write this prime number(2) on the left of the given numbers(12 and 13), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (12, 13) is a multiple of 2, divide it by 2 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 12 and 13 is the product of all prime numbers on the left, i.e. LCM(12, 13) by division method = 2 × 2 × 3 × 13 = 156.

LCM of 12 and 13 by Listing Multiples

LCM of 12 and 13 by Listing Multiples Method

To calculate the LCM of 12 and 13 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 13 (13, 26, 39, 52, 65, . . . . )
  • Step 2: The common multiples from the multiples of 12 and 13 are 156, 312, . . .
  • Step 3: The smallest common multiple of 12 and 13 is 156.

∴ The least common multiple of 12 and 13 = 156.

LCM of 12 and 13 by Prime Factorization

Prime factorization of 12 and 13 is (2 × 2 × 3) = 22 × 31 and (13) = 131 respectively. LCM of 12 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 131 = 156.
Hence, the LCM of 12 and 13 by prime factorization is 156.

☛ Also Check:

LCM of 12 and 13 Examples

  1. Example 1: The product of two numbers is 156. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 156
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 156/1
    Therefore, the LCM is 156.
    The probable combination for the given case is LCM(12, 13) = 156.

  2. Example 2: Verify the relationship between GCF and LCM of 12 and 13.

    Solution:

    The relation between GCF and LCM of 12 and 13 is given as,
    LCM(12, 13) × GCF(12, 13) = Product of 12, 13
    Prime factorization of 12 and 13 is given as, 12 = (2 × 2 × 3) = 22 × 31 and 13 = (13) = 131
    LCM(12, 13) = 156
    GCF(12, 13) = 1
    LHS = LCM(12, 13) × GCF(12, 13) = 156 × 1 = 156
    RHS = Product of 12, 13 = 12 × 13 = 156
    ⇒ LHS = RHS = 156
    Hence, verified.

  3. Example 3: The GCD and LCM of two numbers are 1 and 156 respectively. If one number is 12, find the other number.

    Solution:

    Let the other number be y.
    ∵ GCD × LCM = 12 × y
    ⇒ y = (GCD × LCM)/12
    ⇒ y = (1 × 156)/12
    ⇒ y = 13
    Therefore, the other number is 13.

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FAQs on LCM of 12 and 13

What is the LCM of 12 and 13?

The LCM of 12 and 13 is 156. To find the LCM (least common multiple) of 12 and 13, we need to find the multiples of 12 and 13 (multiples of 12 = 12, 24, 36, 48 . . . . 156; multiples of 13 = 13, 26, 39, 52 . . . . 156) and choose the smallest multiple that is exactly divisible by 12 and 13, i.e., 156.

Which of the following is the LCM of 12 and 13? 156, 35, 15, 42

The value of LCM of 12, 13 is the smallest common multiple of 12 and 13. The number satisfying the given condition is 156.

If the LCM of 13 and 12 is 156, Find its GCF.

LCM(13, 12) × GCF(13, 12) = 13 × 12
Since the LCM of 13 and 12 = 156
⇒ 156 × GCF(13, 12) = 156
Therefore, the greatest common factor (GCF) = 156/156 = 1.

How to Find the LCM of 12 and 13 by Prime Factorization?

To find the LCM of 12 and 13 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (13 = 13). LCM of 12 and 13 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 13.
⇒ LCM of 12, 13 = 22 × 31 × 131 = 156.

What are the Methods to Find LCM of 12 and 13?

The commonly used methods to find the LCM of 12 and 13 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method
 
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