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LCM of 25 and 45

LCM of 25 and 45 is the smallest number among all common multiples of 25 and 45. The first few multiples of 25 and 45 are (25, 50, 75, 100, 125, 150, 175, . . . ) and (45, 90, 135, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 45 - by division method, by listing multiples, and by prime factorization.

1. LCM of 25 and 45
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 25 and 45?

Answer: LCM of 25 and 45 is 225.

LCM of 25 and 45

Explanation:

The LCM of two non-zero integers, x(25) and y(45), is the smallest positive integer m(225) that is divisible by both x(25) and y(45) without any remainder.

Methods to Find LCM of 25 and 45

The methods to find the LCM of 25 and 45 are explained below.

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

LCM of 25 and 45 by Prime Factorization

Prime factorization of 25 and 45 is (5 × 5) = 52 and (3 × 3 × 5) = 32 × 51 respectively. LCM of 25 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 32 × 52 = 225.
Hence, the LCM of 25 and 45 by prime factorization is 225.

LCM of 25 and 45 by Division Method

LCM of 25 and 45 by Division Method

To calculate the LCM of 25 and 45 by the division method, we will divide the numbers(25, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 45.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 45. Write this prime number(3) on the left of the given numbers(25 and 45), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (25, 45) 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 25 and 45 is the product of all prime numbers on the left, i.e. LCM(25, 45) by division method = 3 × 3 × 5 × 5 = 225.

LCM of 25 and 45 by Listing Multiples

To calculate the LCM of 25 and 45 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 25 (25, 50, 75, 100, 125, 150, 175, . . . ) and 45 (45, 90, 135, 180, . . . . )
  • Step 2: The common multiples from the multiples of 25 and 45 are 225, 450, . . .
  • Step 3: The smallest common multiple of 25 and 45 is 225.

∴ The least common multiple of 25 and 45 = 225.

☛ Also Check:

LCM of 25 and 45 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 25 and 45.

    Solution:

    The relation between GCF and LCM of 25 and 45 is given as,
    LCM(25, 45) × GCF(25, 45) = Product of 25, 45
    Prime factorization of 25 and 45 is given as, 25 = (5 × 5) = 52 and 45 = (3 × 3 × 5) = 32 × 51
    LCM(25, 45) = 225
    GCF(25, 45) = 5
    LHS = LCM(25, 45) × GCF(25, 45) = 225 × 5 = 1125
    RHS = Product of 25, 45 = 25 × 45 = 1125
    ⇒ LHS = RHS = 1125
    Hence, verified.

  2. Example 2: The product of two numbers is 1125. If their GCD is 5, what is their LCM?

    Solution:

    Given: GCD = 5
    product of numbers = 1125
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 1125/5
    Therefore, the LCM is 225.
    The probable combination for the given case is LCM(25, 45) = 225.

  3. Example 3: The GCD and LCM of two numbers are 5 and 225 respectively. If one number is 25, find the other number.

    Solution:

    Let the other number be b.
    ∵ GCD × LCM = 25 × b
    ⇒ b = (GCD × LCM)/25
    ⇒ b = (5 × 225)/25
    ⇒ b = 45
    Therefore, the other number is 45.

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FAQs on LCM of 25 and 45

What is the LCM of 25 and 45?

The LCM of 25 and 45 is 225. To find the least common multiple of 25 and 45, we need to find the multiples of 25 and 45 (multiples of 25 = 25, 50, 75, 100 . . . . 225; multiples of 45 = 45, 90, 135, 180 . . . . 225) and choose the smallest multiple that is exactly divisible by 25 and 45, i.e., 225.

If the LCM of 45 and 25 is 225, Find its GCF.

LCM(45, 25) × GCF(45, 25) = 45 × 25
Since the LCM of 45 and 25 = 225
⇒ 225 × GCF(45, 25) = 1125
Therefore, the GCF = 1125/225 = 5.

What is the Least Perfect Square Divisible by 25 and 45?

The least number divisible by 25 and 45 = LCM(25, 45)
LCM of 25 and 45 = 3 × 3 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 25 and 45 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.

What are the Methods to Find LCM of 25 and 45?

The commonly used methods to find the LCM of 25 and 45 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples

Which of the following is the LCM of 25 and 45? 3, 32, 225, 10

The value of LCM of 25, 45 is the smallest common multiple of 25 and 45. The number satisfying the given condition is 225.

 
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