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LCM of 25 and 50
LCM of 25 and 50 is the smallest number among all common multiples of 25 and 50. The first few multiples of 25 and 50 are (25, 50, 75, 100, 125, 150, . . . ) and (50, 100, 150, 200, 250, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 50  by listing multiples, by division method, and by prime factorization.
1.  LCM of 25 and 50 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 25 and 50?
Answer: LCM of 25 and 50 is 50.
Explanation:
The LCM of two nonzero integers, x(25) and y(50), is the smallest positive integer m(50) that is divisible by both x(25) and y(50) without any remainder.
Methods to Find LCM of 25 and 50
The methods to find the LCM of 25 and 50 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 25 and 50 by Division Method
To calculate the LCM of 25 and 50 by the division method, we will divide the numbers(25, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 50.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 50. Write this prime number(2) on the left of the given numbers(25 and 50), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (25, 50) is a multiple of 2, divide it by 2 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 50 is the product of all prime numbers on the left, i.e. LCM(25, 50) by division method = 2 × 5 × 5 = 50.
LCM of 25 and 50 by Listing Multiples
To calculate the LCM of 25 and 50 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, . . . ) and 50 (50, 100, 150, 200, 250, 300, . . . . )
 Step 2: The common multiples from the multiples of 25 and 50 are 50, 100, . . .
 Step 3: The smallest common multiple of 25 and 50 is 50.
∴ The least common multiple of 25 and 50 = 50.
LCM of 25 and 50 by Prime Factorization
Prime factorization of 25 and 50 is (5 × 5) = 5^{2} and (2 × 5 × 5) = 2^{1} × 5^{2} respectively. LCM of 25 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 5^{2} = 50.
Hence, the LCM of 25 and 50 by prime factorization is 50.
☛ Also Check:
 LCM of 15 and 60  60
 LCM of 12, 24 and 36  72
 LCM of 8 and 28  56
 LCM of 20 and 45  180
 LCM of 12, 15 and 21  420
 LCM of 5 and 16  80
 LCM of 9 and 13  117
LCM of 25 and 50 Examples

Example 1: The product of two numbers is 1250. If their GCD is 25, what is their LCM?
Solution:
Given: GCD = 25
product of numbers = 1250
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1250/25
Therefore, the LCM is 50.
The probable combination for the given case is LCM(25, 50) = 50. 
Example 2: Verify the relationship between GCF and LCM of 25 and 50.
Solution:
The relation between GCF and LCM of 25 and 50 is given as,
LCM(25, 50) × GCF(25, 50) = Product of 25, 50
Prime factorization of 25 and 50 is given as, 25 = (5 × 5) = 5^{2} and 50 = (2 × 5 × 5) = 2^{1} × 5^{2}
LCM(25, 50) = 50
GCF(25, 50) = 25
LHS = LCM(25, 50) × GCF(25, 50) = 50 × 25 = 1250
RHS = Product of 25, 50 = 25 × 50 = 1250
⇒ LHS = RHS = 1250
Hence, verified. 
Example 3: Find the smallest number that is divisible by 25 and 50 exactly.
Solution:
The smallest number that is divisible by 25 and 50 exactly is their LCM.
⇒ Multiples of 25 and 50: Multiples of 25 = 25, 50, 75, 100, 125, . . . .
 Multiples of 50 = 50, 100, 150, 200, 250, . . . .
Therefore, the LCM of 25 and 50 is 50.
FAQs on LCM of 25 and 50
What is the LCM of 25 and 50?
The LCM of 25 and 50 is 50. To find the least common multiple of 25 and 50, we need to find the multiples of 25 and 50 (multiples of 25 = 25, 50, 75, 100; multiples of 50 = 50, 100, 150, 200) and choose the smallest multiple that is exactly divisible by 25 and 50, i.e., 50.
If the LCM of 50 and 25 is 50, Find its GCF.
LCM(50, 25) × GCF(50, 25) = 50 × 25
Since the LCM of 50 and 25 = 50
⇒ 50 × GCF(50, 25) = 1250
Therefore, the GCF (greatest common factor) = 1250/50 = 25.
What are the Methods to Find LCM of 25 and 50?
The commonly used methods to find the LCM of 25 and 50 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
What is the Least Perfect Square Divisible by 25 and 50?
The least number divisible by 25 and 50 = LCM(25, 50)
LCM of 25 and 50 = 2 × 5 × 5 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 25 and 50 = LCM(25, 50) × 2 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.
What is the Relation Between GCF and LCM of 25, 50?
The following equation can be used to express the relation between GCF and LCM of 25 and 50, i.e. GCF × LCM = 25 × 50.
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