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LCM of 125 and 75

LCM of 125 and 75 is the smallest number among all common multiples of 125 and 75. The first few multiples of 125 and 75 are (125, 250, 375, 500, 625, 750, . . . ) and (75, 150, 225, 300, 375, 450, 525, . . . ) respectively. There are 3 commonly used methods to find LCM of 125 and 75 - by listing multiples, by division method, and by prime factorization.

1. LCM of 125 and 75
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 125 and 75?

Answer: LCM of 125 and 75 is 375.

LCM of 125 and 75

Explanation:

The LCM of two non-zero integers, x(125) and y(75), is the smallest positive integer m(375) that is divisible by both x(125) and y(75) without any remainder.

Methods to Find LCM of 125 and 75

The methods to find the LCM of 125 and 75 are explained below.

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

LCM of 125 and 75 by Division Method

LCM of 125 and 75 by Division Method

To calculate the LCM of 125 and 75 by the division method, we will divide the numbers(125, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 125 and 75.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 125 and 75. Write this prime number(3) on the left of the given numbers(125 and 75), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (125, 75) 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 125 and 75 is the product of all prime numbers on the left, i.e. LCM(125, 75) by division method = 3 × 5 × 5 × 5 = 375.

LCM of 125 and 75 by Listing Multiples

To calculate the LCM of 125 and 75 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 125 (125, 250, 375, 500, 625, 750, . . . ) and 75 (75, 150, 225, 300, 375, 450, 525, . . . . )
  • Step 2: The common multiples from the multiples of 125 and 75 are 375, 750, . . .
  • Step 3: The smallest common multiple of 125 and 75 is 375.

∴ The least common multiple of 125 and 75 = 375.

LCM of 125 and 75 by Prime Factorization

Prime factorization of 125 and 75 is (5 × 5 × 5) = 53 and (3 × 5 × 5) = 31 × 52 respectively. LCM of 125 and 75 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 31 × 53 = 375.
Hence, the LCM of 125 and 75 by prime factorization is 375.

☛ Also Check:

LCM of 125 and 75 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 125 and 75.

    Solution:

    The relation between GCF and LCM of 125 and 75 is given as,
    LCM(125, 75) × GCF(125, 75) = Product of 125, 75
    Prime factorization of 125 and 75 is given as, 125 = (5 × 5 × 5) = 53 and 75 = (3 × 5 × 5) = 31 × 52
    LCM(125, 75) = 375
    GCF(125, 75) = 25
    LHS = LCM(125, 75) × GCF(125, 75) = 375 × 25 = 9375
    RHS = Product of 125, 75 = 125 × 75 = 9375
    ⇒ LHS = RHS = 9375
    Hence, verified.

  2. Example 2: The product of two numbers is 9375. If their GCD is 25, what is their LCM?

    Solution:

    Given: GCD = 25
    product of numbers = 9375
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 9375/25
    Therefore, the LCM is 375.
    The probable combination for the given case is LCM(125, 75) = 375.

  3. Example 3: The GCD and LCM of two numbers are 25 and 375 respectively. If one number is 75, find the other number.

    Solution:

    Let the other number be b.
    ∵ GCD × LCM = 75 × b
    ⇒ b = (GCD × LCM)/75
    ⇒ b = (25 × 375)/75
    ⇒ b = 125
    Therefore, the other number is 125.

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FAQs on LCM of 125 and 75

What is the LCM of 125 and 75?

The LCM of 125 and 75 is 375. To find the least common multiple of 125 and 75, we need to find the multiples of 125 and 75 (multiples of 125 = 125, 250, 375, 500; multiples of 75 = 75, 150, 225, 300 . . . . 375) and choose the smallest multiple that is exactly divisible by 125 and 75, i.e., 375.

If the LCM of 75 and 125 is 375, Find its GCF.

LCM(75, 125) × GCF(75, 125) = 75 × 125
Since the LCM of 75 and 125 = 375
⇒ 375 × GCF(75, 125) = 9375
Therefore, the GCF (greatest common factor) = 9375/375 = 25.

What are the Methods to Find LCM of 125 and 75?

The commonly used methods to find the LCM of 125 and 75 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

Which of the following is the LCM of 125 and 75? 50, 375, 3, 10

The value of LCM of 125, 75 is the smallest common multiple of 125 and 75. The number satisfying the given condition is 375.

What is the Relation Between GCF and LCM of 125, 75?

The following equation can be used to express the relation between GCF and LCM of 125 and 75, i.e. GCF × LCM = 125 × 75.

 
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