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LCM of 125 and 175

LCM of 125 and 175 is the smallest number among all common multiples of 125 and 175. The first few multiples of 125 and 175 are (125, 250, 375, 500, . . . ) and (175, 350, 525, 700, 875, 1050, 1225, . . . ) respectively. There are 3 commonly used methods to find LCM of 125 and 175 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 125 and 175
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 125 and 175?

Answer: LCM of 125 and 175 is 875.

Explanation:

The LCM of two non-zero integers, x(125) and y(175), is the smallest positive integer m(875) that is divisible by both x(125) and y(175) without any remainder.

Methods to Find LCM of 125 and 175

Let's look at the different methods for finding the LCM of 125 and 175.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 125 and 175 by Prime Factorization

Prime factorization of 125 and 175 is (5 × 5 × 5) = 5³ and (5 × 5 × 7) = 5² × 7¹ respectively. LCM of 125 and 175 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 5³ × 7¹ = 875.
Hence, the LCM of 125 and 175 by prime factorization is 875.

LCM of 125 and 175 by Division Method

To calculate the LCM of 125 and 175 by the division method, we will divide the numbers(125, 175) by their prime factors (preferably common). The product of these divisors gives the LCM of 125 and 175.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 125 and 175. Write this prime number(5) on the left of the given numbers(125 and 175), separated as per the ladder arrangement.
Step 2: If any of the given numbers (125, 175) is a multiple of 5, divide it by 5 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 175 is the product of all prime numbers on the left, i.e. LCM(125, 175) by division method = 5 × 5 × 5 × 7 = 875.

LCM of 125 and 175 by Listing Multiples

To calculate the LCM of 125 and 175 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, . . . ) and 175 (175, 350, 525, 700, 875, 1050, 1225, . . . . )
Step 2: The common multiples from the multiples of 125 and 175 are 875, 1750, . . .
Step 3: The smallest common multiple of 125 and 175 is 875.

∴ The least common multiple of 125 and 175 = 875.

☛ Also Check:

LCM of 125 and 175 Examples

Example 1: The GCD and LCM of two numbers are 25 and 875 respectively. If one number is 175, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 175 × a
⇒ a = (GCD × LCM)/175
⇒ a = (25 × 875)/175
⇒ a = 125
Therefore, the other number is 125.
Example 2: The product of two numbers is 21875. If their GCD is 25, what is their LCM?

Solution:

Given: GCD = 25
product of numbers = 21875
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 21875/25
Therefore, the LCM is 875.
The probable combination for the given case is LCM(125, 175) = 875.
Example 3: Verify the relationship between GCF and LCM of 125 and 175.

Solution:

The relation between GCF and LCM of 125 and 175 is given as,
LCM(125, 175) × GCF(125, 175) = Product of 125, 175
Prime factorization of 125 and 175 is given as, 125 = (5 × 5 × 5) = 5³ and 175 = (5 × 5 × 7) = 5² × 7¹
LCM(125, 175) = 875
GCF(125, 175) = 25
LHS = LCM(125, 175) × GCF(125, 175) = 875 × 25 = 21875
RHS = Product of 125, 175 = 125 × 175 = 21875
⇒ LHS = RHS = 21875
Hence, verified.

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FAQs on LCM of 125 and 175

What is the LCM of 125 and 175?

The LCM of 125 and 175 is 875. To find the LCM of 125 and 175, we need to find the multiples of 125 and 175 (multiples of 125 = 125, 250, 375, 500 . . . . 875; multiples of 175 = 175, 350, 525, 700 . . . . 875) and choose the smallest multiple that is exactly divisible by 125 and 175, i.e., 875.

If the LCM of 175 and 125 is 875, Find its GCF.

LCM(175, 125) × GCF(175, 125) = 175 × 125
Since the LCM of 175 and 125 = 875
⇒ 875 × GCF(175, 125) = 21875
Therefore, the greatest common factor (GCF) = 21875/875 = 25.

Which of the following is the LCM of 125 and 175? 27, 16, 42, 875

The value of LCM of 125, 175 is the smallest common multiple of 125 and 175. The number satisfying the given condition is 875.

What is the Relation Between GCF and LCM of 125, 175?

The following equation can be used to express the relation between GCF and LCM of 125 and 175, i.e. GCF × LCM = 125 × 175.

What is the Least Perfect Square Divisible by 125 and 175?

The least number divisible by 125 and 175 = LCM(125, 175)
LCM of 125 and 175 = 5 × 5 × 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 125 and 175 = LCM(125, 175) × 5 × 7 = 30625 [Square root of 30625 = √30625 = ±175]
Therefore, 30625 is the required number.

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