LCM of 25 and 75
LCM of 25 and 75 is the smallest number among all common multiples of 25 and 75. The first few multiples of 25 and 75 are (25, 50, 75, 100, . . . ) and (75, 150, 225, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 75  by division method, by listing multiples, and by prime factorization.
1.  LCM of 25 and 75 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 25 and 75?
Answer: LCM of 25 and 75 is 75.
Explanation:
The LCM of two nonzero integers, x(25) and y(75), is the smallest positive integer m(75) that is divisible by both x(25) and y(75) without any remainder.
Methods to Find LCM of 25 and 75
The methods to find the LCM of 25 and 75 are explained below.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 25 and 75 by Listing Multiples
To calculate the LCM of 25 and 75 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, . . . ) and 75 (75, 150, 225, 300, . . . . )
 Step 2: The common multiples from the multiples of 25 and 75 are 75, 150, . . .
 Step 3: The smallest common multiple of 25 and 75 is 75.
∴ The least common multiple of 25 and 75 = 75.
LCM of 25 and 75 by Prime Factorization
Prime factorization of 25 and 75 is (5 × 5) = 5^{2} and (3 × 5 × 5) = 3^{1} × 5^{2} respectively. LCM of 25 and 75 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{1} × 5^{2} = 75.
Hence, the LCM of 25 and 75 by prime factorization is 75.
LCM of 25 and 75 by Division Method
To calculate the LCM of 25 and 75 by the division method, we will divide the numbers(25, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 75.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 75. Write this prime number(3) on the left of the given numbers(25 and 75), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (25, 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 25 and 75 is the product of all prime numbers on the left, i.e. LCM(25, 75) by division method = 3 × 5 × 5 = 75.
☛ Also Check:
 LCM of 6, 8 and 12  24
 LCM of 3, 4 and 7  84
 LCM of 24 and 8  24
 LCM of 3, 4 and 6  12
 LCM of 60 and 62  1860
 LCM of 16, 20 and 24  240
 LCM of 21 and 24  168
LCM of 25 and 75 Examples

Example 1: The product of two numbers is 1875. If their GCD is 25, what is their LCM?
Solution:
Given: GCD = 25
product of numbers = 1875
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1875/25
Therefore, the LCM is 75.
The probable combination for the given case is LCM(25, 75) = 75. 
Example 2: Find the smallest number that is divisible by 25 and 75 exactly.
Solution:
The smallest number that is divisible by 25 and 75 exactly is their LCM.
⇒ Multiples of 25 and 75: Multiples of 25 = 25, 50, 75, 100, 125, . . . .
 Multiples of 75 = 75, 150, 225, 300, 375, . . . .
Therefore, the LCM of 25 and 75 is 75.

Example 3: The GCD and LCM of two numbers are 25 and 75 respectively. If one number is 25, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 25 × m
⇒ m = (GCD × LCM)/25
⇒ m = (25 × 75)/25
⇒ m = 75
Therefore, the other number is 75.
FAQs on LCM of 25 and 75
What is the LCM of 25 and 75?
The LCM of 25 and 75 is 75. To find the LCM (least common multiple) of 25 and 75, we need to find the multiples of 25 and 75 (multiples of 25 = 25, 50, 75, 100; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 25 and 75, i.e., 75.
What is the Least Perfect Square Divisible by 25 and 75?
The least number divisible by 25 and 75 = LCM(25, 75)
LCM of 25 and 75 = 3 × 5 × 5 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 25 and 75 = LCM(25, 75) × 3 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.
What are the Methods to Find LCM of 25 and 75?
The commonly used methods to find the LCM of 25 and 75 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
If the LCM of 75 and 25 is 75, Find its GCF.
LCM(75, 25) × GCF(75, 25) = 75 × 25
Since the LCM of 75 and 25 = 75
⇒ 75 × GCF(75, 25) = 1875
Therefore, the greatest common factor (GCF) = 1875/75 = 25.
What is the Relation Between GCF and LCM of 25, 75?
The following equation can be used to express the relation between GCF and LCM of 25 and 75, i.e. GCF × LCM = 25 × 75.
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