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LCM of 9 and 25

LCM of 9 and 25 is the smallest number among all common multiples of 9 and 25. The first few multiples of 9 and 25 are (9, 18, 27, 36, 45, 54, 63, . . . ) and (25, 50, 75, 100, 125, 150, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 25 - by prime factorization, by division method, and by listing multiples.

1. LCM of 9 and 25
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 9 and 25?

Answer: LCM of 9 and 25 is 225.

LCM of 9 and 25

Explanation:

The LCM of two non-zero integers, x(9) and y(25), is the smallest positive integer m(225) that is divisible by both x(9) and y(25) without any remainder.

Methods to Find LCM of 9 and 25

The methods to find the LCM of 9 and 25 are explained below.

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

LCM of 9 and 25 by Division Method

LCM of 9 and 25 by Division Method

To calculate the LCM of 9 and 25 by the division method, we will divide the numbers(9, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 25.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 25. Write this prime number(3) on the left of the given numbers(9 and 25), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (9, 25) 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 9 and 25 is the product of all prime numbers on the left, i.e. LCM(9, 25) by division method = 3 × 3 × 5 × 5 = 225.

LCM of 9 and 25 by Listing Multiples

To calculate the LCM of 9 and 25 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, 63, . . . ) and 25 (25, 50, 75, 100, 125, 150, . . . . )
  • Step 2: The common multiples from the multiples of 9 and 25 are 225, 450, . . .
  • Step 3: The smallest common multiple of 9 and 25 is 225.

∴ The least common multiple of 9 and 25 = 225.

LCM of 9 and 25 by Prime Factorization

Prime factorization of 9 and 25 is (3 × 3) = 32 and (5 × 5) = 52 respectively. LCM of 9 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 32 × 52 = 225.
Hence, the LCM of 9 and 25 by prime factorization is 225.

☛ Also Check:

LCM of 9 and 25 Examples

  1. Example 1: The product of two numbers is 225. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 225
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 225/1
    Therefore, the LCM is 225.
    The probable combination for the given case is LCM(9, 25) = 225.

  2. Example 2: Verify the relationship between GCF and LCM of 9 and 25.

    Solution:

    The relation between GCF and LCM of 9 and 25 is given as,
    LCM(9, 25) × GCF(9, 25) = Product of 9, 25
    Prime factorization of 9 and 25 is given as, 9 = (3 × 3) = 32 and 25 = (5 × 5) = 52
    LCM(9, 25) = 225
    GCF(9, 25) = 1
    LHS = LCM(9, 25) × GCF(9, 25) = 225 × 1 = 225
    RHS = Product of 9, 25 = 9 × 25 = 225
    ⇒ LHS = RHS = 225
    Hence, verified.

  3. Example 3: Find the smallest number that is divisible by 9 and 25 exactly.

    Solution:

    The value of LCM(9, 25) will be the smallest number that is exactly divisible by 9 and 25.
    ⇒ Multiples of 9 and 25:

    • Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 189, 198, 207, 216, 225, . . . .
    • Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 175, 200, 225, . . . .

    Therefore, the LCM of 9 and 25 is 225.

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FAQs on LCM of 9 and 25

What is the LCM of 9 and 25?

The LCM of 9 and 25 is 225. To find the least common multiple of 9 and 25, we need to find the multiples of 9 and 25 (multiples of 9 = 9, 18, 27, 36 . . . . 225; multiples of 25 = 25, 50, 75, 100 . . . . 225) and choose the smallest multiple that is exactly divisible by 9 and 25, i.e., 225.

Which of the following is the LCM of 9 and 25? 225, 50, 20, 35

The value of LCM of 9, 25 is the smallest common multiple of 9 and 25. The number satisfying the given condition is 225.

What are the Methods to Find LCM of 9 and 25?

The commonly used methods to find the LCM of 9 and 25 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

What is the Relation Between GCF and LCM of 9, 25?

The following equation can be used to express the relation between GCF and LCM of 9 and 25, i.e. GCF × LCM = 9 × 25.

If the LCM of 25 and 9 is 225, Find its GCF.

LCM(25, 9) × GCF(25, 9) = 25 × 9
Since the LCM of 25 and 9 = 225
⇒ 225 × GCF(25, 9) = 225
Therefore, the GCF = 225/225 = 1.

 
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