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LCM of 12 and 80

LCM of 12 and 80 is the smallest number among all common multiples of 12 and 80. The first few multiples of 12 and 80 are (12, 24, 36, 48, 60, . . . ) and (80, 160, 240, 320, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 80 - by division method, by listing multiples, and by prime factorization.

1. LCM of 12 and 80
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 12 and 80?

Answer: LCM of 12 and 80 is 240.

LCM of 12 and 80

Explanation:

The LCM of two non-zero integers, x(12) and y(80), is the smallest positive integer m(240) that is divisible by both x(12) and y(80) without any remainder.

Methods to Find LCM of 12 and 80

Let's look at the different methods for finding the LCM of 12 and 80.

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

LCM of 12 and 80 by Division Method

LCM of 12 and 80 by Division Method

To calculate the LCM of 12 and 80 by the division method, we will divide the numbers(12, 80) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 80.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 80. Write this prime number(2) on the left of the given numbers(12 and 80), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (12, 80) 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 80 is the product of all prime numbers on the left, i.e. LCM(12, 80) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

LCM of 12 and 80 by Prime Factorization

Prime factorization of 12 and 80 is (2 × 2 × 3) = 22 × 31 and (2 × 2 × 2 × 2 × 5) = 24 × 51 respectively. LCM of 12 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 31 × 51 = 240.
Hence, the LCM of 12 and 80 by prime factorization is 240.

LCM of 12 and 80 by Listing Multiples

To calculate the LCM of 12 and 80 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, . . . ) and 80 (80, 160, 240, 320, . . . . )
  • Step 2: The common multiples from the multiples of 12 and 80 are 240, 480, . . .
  • Step 3: The smallest common multiple of 12 and 80 is 240.

∴ The least common multiple of 12 and 80 = 240.

☛ Also Check:

LCM of 12 and 80 Examples

  1. Example 1: The GCD and LCM of two numbers are 4 and 240 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 = (4 × 240)/12
    ⇒ y = 80
    Therefore, the other number is 80.

  2. Example 2: Verify the relationship between GCF and LCM of 12 and 80.

    Solution:

    The relation between GCF and LCM of 12 and 80 is given as,
    LCM(12, 80) × GCF(12, 80) = Product of 12, 80
    Prime factorization of 12 and 80 is given as, 12 = (2 × 2 × 3) = 22 × 31 and 80 = (2 × 2 × 2 × 2 × 5) = 24 × 51
    LCM(12, 80) = 240
    GCF(12, 80) = 4
    LHS = LCM(12, 80) × GCF(12, 80) = 240 × 4 = 960
    RHS = Product of 12, 80 = 12 × 80 = 960
    ⇒ LHS = RHS = 960
    Hence, verified.

  3. Example 3: Find the smallest number that is divisible by 12 and 80 exactly.

    Solution:

    The value of LCM(12, 80) will be the smallest number that is exactly divisible by 12 and 80.
    ⇒ Multiples of 12 and 80:

    • Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 216, 228, 240, . . . .
    • Multiples of 80 = 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, . . . ., -80, 0, 80, 160, 240, . . . .

    Therefore, the LCM of 12 and 80 is 240.

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FAQs on LCM of 12 and 80

What is the LCM of 12 and 80?

The LCM of 12 and 80 is 240. To find the LCM of 12 and 80, we need to find the multiples of 12 and 80 (multiples of 12 = 12, 24, 36, 48 . . . . 240; multiples of 80 = 80, 160, 240, 320) and choose the smallest multiple that is exactly divisible by 12 and 80, i.e., 240.

What are the Methods to Find LCM of 12 and 80?

The commonly used methods to find the LCM of 12 and 80 are:

  • Division Method
  • Listing Multiples
  • Prime Factorization Method

If the LCM of 80 and 12 is 240, Find its GCF.

LCM(80, 12) × GCF(80, 12) = 80 × 12
Since the LCM of 80 and 12 = 240
⇒ 240 × GCF(80, 12) = 960
Therefore, the greatest common factor (GCF) = 960/240 = 4.

Which of the following is the LCM of 12 and 80? 27, 50, 21, 240

The value of LCM of 12, 80 is the smallest common multiple of 12 and 80. The number satisfying the given condition is 240.

What is the Relation Between GCF and LCM of 12, 80?

The following equation can be used to express the relation between GCF and LCM of 12 and 80, i.e. GCF × LCM = 12 × 80.

 
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