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LCM of 12 and 36

LCM of 12 and 36 is the smallest number among all common multiples of 12 and 36. The first few multiples of 12 and 36 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (36, 72, 108, 144, 180, 216, 252, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 36 - by listing multiples, by prime factorization, and by division method.

1. LCM of 12 and 36
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 12 and 36?

Answer: LCM of 12 and 36 is 36.

LCM of 12 and 36

Explanation:

The LCM of two non-zero integers, x(12) and y(36), is the smallest positive integer m(36) that is divisible by both x(12) and y(36) without any remainder.

Methods to Find LCM of 12 and 36

The methods to find the LCM of 12 and 36 are explained below.

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

LCM of 12 and 36 by Prime Factorization

Prime factorization of 12 and 36 is (2 × 2 × 3) = 22 × 31 and (2 × 2 × 3 × 3) = 22 × 32 respectively. LCM of 12 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 = 36.
Hence, the LCM of 12 and 36 by prime factorization is 36.

LCM of 12 and 36 by Division Method

LCM of 12 and 36 by Division Method

To calculate the LCM of 12 and 36 by the division method, we will divide the numbers(12, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 36.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 36. Write this prime number(2) on the left of the given numbers(12 and 36), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (12, 36) 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 36 is the product of all prime numbers on the left, i.e. LCM(12, 36) by division method = 2 × 2 × 3 × 3 = 36.

LCM of 12 and 36 by Listing Multiples

To calculate the LCM of 12 and 36 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, 84, . . . ) and 36 (36, 72, 108, 144, 180, 216, 252, . . . . )
  • Step 2: The common multiples from the multiples of 12 and 36 are 36, 72, . . .
  • Step 3: The smallest common multiple of 12 and 36 is 36.

∴ The least common multiple of 12 and 36 = 36.

☛ Also Check:

LCM of 12 and 36 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 12 and 36.

    Solution:

    The relation between GCF and LCM of 12 and 36 is given as,
    LCM(12, 36) × GCF(12, 36) = Product of 12, 36
    Prime factorization of 12 and 36 is given as, 12 = (2 × 2 × 3) = 22 × 31 and 36 = (2 × 2 × 3 × 3) = 22 × 32
    LCM(12, 36) = 36
    GCF(12, 36) = 12
    LHS = LCM(12, 36) × GCF(12, 36) = 36 × 12 = 432
    RHS = Product of 12, 36 = 12 × 36 = 432
    ⇒ LHS = RHS = 432
    Hence, verified.

  2. Example 2: The GCD and LCM of two numbers are 12 and 36 respectively. If one number is 12, find the other number.

    Solution:

    Let the other number be a.
    ∵ GCD × LCM = 12 × a
    ⇒ a = (GCD × LCM)/12
    ⇒ a = (12 × 36)/12
    ⇒ a = 36
    Therefore, the other number is 36.

  3. Example 3: Find the smallest number that is divisible by 12 and 36 exactly.

    Solution:

    The smallest number that is divisible by 12 and 36 exactly is their LCM.
    ⇒ Multiples of 12 and 36:

    • Multiples of 12 = 12, 24, 36, 48, 60, 72, . . . .
    • Multiples of 36 = 36, 72, 108, 144, 180, 216, . . . .

    Therefore, the LCM of 12 and 36 is 36.

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FAQs on LCM of 12 and 36

What is the LCM of 12 and 36?

The LCM of 12 and 36 is 36. To find the LCM (least common multiple) of 12 and 36, we need to find the multiples of 12 and 36 (multiples of 12 = 12, 24, 36, 48; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 12 and 36, i.e., 36.

What are the Methods to Find LCM of 12 and 36?

The commonly used methods to find the LCM of 12 and 36 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

Which of the following is the LCM of 12 and 36? 2, 25, 5, 36

The value of LCM of 12, 36 is the smallest common multiple of 12 and 36. The number satisfying the given condition is 36.

If the LCM of 36 and 12 is 36, Find its GCF.

LCM(36, 12) × GCF(36, 12) = 36 × 12
Since the LCM of 36 and 12 = 36
⇒ 36 × GCF(36, 12) = 432
Therefore, the GCF (greatest common factor) = 432/36 = 12.

What is the Relation Between GCF and LCM of 12, 36?

The following equation can be used to express the relation between GCF and LCM of 12 and 36, i.e. GCF × LCM = 12 × 36.

 
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