LCM of 5 and 25
LCM of 5 and 25 is the smallest number among all common multiples of 5 and 25. The first few multiples of 5 and 25 are (5, 10, 15, 20, 25, 30, . . . ) and (25, 50, 75, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 25  by listing multiples, by division method, and by prime factorization.
1.  LCM of 5 and 25 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 5 and 25?
Answer: LCM of 5 and 25 is 25.
Explanation:
The LCM of two nonzero integers, x(5) and y(25), is the smallest positive integer m(25) that is divisible by both x(5) and y(25) without any remainder.
Methods to Find LCM of 5 and 25
Let's look at the different methods for finding the LCM of 5 and 25.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 5 and 25 by Division Method
To calculate the LCM of 5 and 25 by the division method, we will divide the numbers(5, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 25.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 25. Write this prime number(5) on the left of the given numbers(5 and 25), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (5, 25) 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 5 and 25 is the product of all prime numbers on the left, i.e. LCM(5, 25) by division method = 5 × 5 = 25.
LCM of 5 and 25 by Prime Factorization
Prime factorization of 5 and 25 is (5) = 5^{1} and (5 × 5) = 5^{2} respectively. LCM of 5 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 5^{2} = 25.
Hence, the LCM of 5 and 25 by prime factorization is 25.
LCM of 5 and 25 by Listing Multiples
To calculate the LCM of 5 and 25 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 25 (25, 50, 75, 100, . . . . )
 Step 2: The common multiples from the multiples of 5 and 25 are 25, 50, . . .
 Step 3: The smallest common multiple of 5 and 25 is 25.
∴ The least common multiple of 5 and 25 = 25.
☛ Also Check:
 LCM of 12 and 42  84
 LCM of 6 and 21  42
 LCM of 850 and 680  3400
 LCM of 4, 8 and 12  24
 LCM of 2, 3, 4, 5, 6 and 7  420
 LCM of 6 and 7  42
 LCM of 18 and 20  180
LCM of 5 and 25 Examples

Example 1: Verify the relationship between GCF and LCM of 5 and 25.
Solution:
The relation between GCF and LCM of 5 and 25 is given as,
LCM(5, 25) × GCF(5, 25) = Product of 5, 25
Prime factorization of 5 and 25 is given as, 5 = (5) = 5^{1} and 25 = (5 × 5) = 5^{2}
LCM(5, 25) = 25
GCF(5, 25) = 5
LHS = LCM(5, 25) × GCF(5, 25) = 25 × 5 = 125
RHS = Product of 5, 25 = 5 × 25 = 125
⇒ LHS = RHS = 125
Hence, verified. 
Example 2: The product of two numbers is 125. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 125
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 125/5
Therefore, the LCM is 25.
The probable combination for the given case is LCM(5, 25) = 25. 
Example 3: The GCD and LCM of two numbers are 5 and 25 respectively. If one number is 25, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 25 × a
⇒ a = (GCD × LCM)/25
⇒ a = (5 × 25)/25
⇒ a = 5
Therefore, the other number is 5.
FAQs on LCM of 5 and 25
What is the LCM of 5 and 25?
The LCM of 5 and 25 is 25. To find the least common multiple (LCM) of 5 and 25, we need to find the multiples of 5 and 25 (multiples of 5 = 5, 10, 15, 20 . . . . 25; multiples of 25 = 25, 50, 75, 100) and choose the smallest multiple that is exactly divisible by 5 and 25, i.e., 25.
What is the Least Perfect Square Divisible by 5 and 25?
The least number divisible by 5 and 25 = LCM(5, 25)
LCM of 5 and 25 = 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 5 and 25 = 25 [Square root of 25 = √25 = ±5]
Therefore, 25 is the required number.
What is the Relation Between GCF and LCM of 5, 25?
The following equation can be used to express the relation between GCF and LCM of 5 and 25, i.e. GCF × LCM = 5 × 25.
How to Find the LCM of 5 and 25 by Prime Factorization?
To find the LCM of 5 and 25 using prime factorization, we will find the prime factors, (5 = 5) and (25 = 5 × 5). LCM of 5 and 25 is the product of prime factors raised to their respective highest exponent among the numbers 5 and 25.
⇒ LCM of 5, 25 = 5^{2} = 25.
If the LCM of 25 and 5 is 25, Find its GCF.
LCM(25, 5) × GCF(25, 5) = 25 × 5
Since the LCM of 25 and 5 = 25
⇒ 25 × GCF(25, 5) = 125
Therefore, the greatest common factor (GCF) = 125/25 = 5.
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