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LCM of 144 and 180

LCM of 144 and 180 is the smallest number among all common multiples of 144 and 180. The first few multiples of 144 and 180 are (144, 288, 432, 576, 720, . . . ) and (180, 360, 540, 720, 900, 1080, 1260, . . . ) respectively. There are 3 commonly used methods to find LCM of 144 and 180 - by division method, by prime factorization, and by listing multiples.

1. LCM of 144 and 180
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 144 and 180?

Answer: LCM of 144 and 180 is 720.

LCM of 144 and 180

Explanation:

The LCM of two non-zero integers, x(144) and y(180), is the smallest positive integer m(720) that is divisible by both x(144) and y(180) without any remainder.

Methods to Find LCM of 144 and 180

The methods to find the LCM of 144 and 180 are explained below.

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

LCM of 144 and 180 by Prime Factorization

Prime factorization of 144 and 180 is (2 × 2 × 2 × 2 × 3 × 3) = 24 × 32 and (2 × 2 × 3 × 3 × 5) = 22 × 32 × 51 respectively. LCM of 144 and 180 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 32 × 51 = 720.
Hence, the LCM of 144 and 180 by prime factorization is 720.

LCM of 144 and 180 by Division Method

LCM of 144 and 180 by Division Method

To calculate the LCM of 144 and 180 by the division method, we will divide the numbers(144, 180) by their prime factors (preferably common). The product of these divisors gives the LCM of 144 and 180.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 144 and 180. Write this prime number(2) on the left of the given numbers(144 and 180), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (144, 180) 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 144 and 180 is the product of all prime numbers on the left, i.e. LCM(144, 180) by division method = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720.

LCM of 144 and 180 by Listing Multiples

To calculate the LCM of 144 and 180 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 144 (144, 288, 432, 576, 720, . . . ) and 180 (180, 360, 540, 720, 900, 1080, 1260, . . . . )
  • Step 2: The common multiples from the multiples of 144 and 180 are 720, 1440, . . .
  • Step 3: The smallest common multiple of 144 and 180 is 720.

∴ The least common multiple of 144 and 180 = 720.

☛ Also Check:

LCM of 144 and 180 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 144 and 180.

    Solution:

    The relation between GCF and LCM of 144 and 180 is given as,
    LCM(144, 180) × GCF(144, 180) = Product of 144, 180
    Prime factorization of 144 and 180 is given as, 144 = (2 × 2 × 2 × 2 × 3 × 3) = 24 × 32 and 180 = (2 × 2 × 3 × 3 × 5) = 22 × 32 × 51
    LCM(144, 180) = 720
    GCF(144, 180) = 36
    LHS = LCM(144, 180) × GCF(144, 180) = 720 × 36 = 25920
    RHS = Product of 144, 180 = 144 × 180 = 25920
    ⇒ LHS = RHS = 25920
    Hence, verified.

  2. Example 2: The GCD and LCM of two numbers are 36 and 720 respectively. If one number is 144, find the other number.

    Solution:

    Let the other number be m.
    ∵ GCD × LCM = 144 × m
    ⇒ m = (GCD × LCM)/144
    ⇒ m = (36 × 720)/144
    ⇒ m = 180
    Therefore, the other number is 180.

  3. Example 3: The product of two numbers is 25920. If their GCD is 36, what is their LCM?

    Solution:

    Given: GCD = 36
    product of numbers = 25920
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 25920/36
    Therefore, the LCM is 720.
    The probable combination for the given case is LCM(144, 180) = 720.

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FAQs on LCM of 144 and 180

What is the LCM of 144 and 180?

The LCM of 144 and 180 is 720. To find the least common multiple (LCM) of 144 and 180, we need to find the multiples of 144 and 180 (multiples of 144 = 144, 288, 432, 576 . . . . 720; multiples of 180 = 180, 360, 540, 720) and choose the smallest multiple that is exactly divisible by 144 and 180, i.e., 720.

What is the Relation Between GCF and LCM of 144, 180?

The following equation can be used to express the relation between GCF and LCM of 144 and 180, i.e. GCF × LCM = 144 × 180.

Which of the following is the LCM of 144 and 180? 36, 21, 720, 45

The value of LCM of 144, 180 is the smallest common multiple of 144 and 180. The number satisfying the given condition is 720.

What are the Methods to Find LCM of 144 and 180?

The commonly used methods to find the LCM of 144 and 180 are:

  • Division Method
  • Listing Multiples
  • Prime Factorization Method

If the LCM of 180 and 144 is 720, Find its GCF.

LCM(180, 144) × GCF(180, 144) = 180 × 144
Since the LCM of 180 and 144 = 720
⇒ 720 × GCF(180, 144) = 25920
Therefore, the greatest common factor (GCF) = 25920/720 = 36.

 
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