LCM of 25 and 60
LCM of 25 and 60 is the smallest number among all common multiples of 25 and 60. The first few multiples of 25 and 60 are (25, 50, 75, 100, 125, . . . ) and (60, 120, 180, 240, 300, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 60  by division method, by listing multiples, and by prime factorization.
1.  LCM of 25 and 60 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 25 and 60?
Answer: LCM of 25 and 60 is 300.
Explanation:
The LCM of two nonzero integers, x(25) and y(60), is the smallest positive integer m(300) that is divisible by both x(25) and y(60) without any remainder.
Methods to Find LCM of 25 and 60
The methods to find the LCM of 25 and 60 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 25 and 60 by Division Method
To calculate the LCM of 25 and 60 by the division method, we will divide the numbers(25, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 60.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 60. Write this prime number(2) on the left of the given numbers(25 and 60), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (25, 60) 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 60 is the product of all prime numbers on the left, i.e. LCM(25, 60) by division method = 2 × 2 × 3 × 5 × 5 = 300.
LCM of 25 and 60 by Prime Factorization
Prime factorization of 25 and 60 is (5 × 5) = 5^{2} and (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1} respectively. LCM of 25 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 5^{2} = 300.
Hence, the LCM of 25 and 60 by prime factorization is 300.
LCM of 25 and 60 by Listing Multiples
To calculate the LCM of 25 and 60 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, . . . ) and 60 (60, 120, 180, 240, 300, 360, . . . . )
 Step 2: The common multiples from the multiples of 25 and 60 are 300, 600, . . .
 Step 3: The smallest common multiple of 25 and 60 is 300.
∴ The least common multiple of 25 and 60 = 300.
☛ Also Check:
 LCM of 20 and 25  100
 LCM of 5, 8 and 12  120
 LCM of 13 and 17  221
 LCM of 42 and 63  126
 LCM of 30 and 35  210
 LCM of 20, 40 and 60  120
 LCM of 12 and 60  60
LCM of 25 and 60 Examples

Example 1: The GCD and LCM of two numbers are 5 and 300 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 = (5 × 300)/25
⇒ m = 60
Therefore, the other number is 60. 
Example 2: Find the smallest number that is divisible by 25 and 60 exactly.
Solution:
The smallest number that is divisible by 25 and 60 exactly is their LCM.
⇒ Multiples of 25 and 60: Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, . . . .
 Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, . . . .
Therefore, the LCM of 25 and 60 is 300.

Example 3: Verify the relationship between GCF and LCM of 25 and 60.
Solution:
The relation between GCF and LCM of 25 and 60 is given as,
LCM(25, 60) × GCF(25, 60) = Product of 25, 60
Prime factorization of 25 and 60 is given as, 25 = (5 × 5) = 5^{2} and 60 = (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1}
LCM(25, 60) = 300
GCF(25, 60) = 5
LHS = LCM(25, 60) × GCF(25, 60) = 300 × 5 = 1500
RHS = Product of 25, 60 = 25 × 60 = 1500
⇒ LHS = RHS = 1500
Hence, verified.
FAQs on LCM of 25 and 60
What is the LCM of 25 and 60?
The LCM of 25 and 60 is 300. To find the least common multiple of 25 and 60, we need to find the multiples of 25 and 60 (multiples of 25 = 25, 50, 75, 100 . . . . 300; multiples of 60 = 60, 120, 180, 240 . . . . 300) and choose the smallest multiple that is exactly divisible by 25 and 60, i.e., 300.
How to Find the LCM of 25 and 60 by Prime Factorization?
To find the LCM of 25 and 60 using prime factorization, we will find the prime factors, (25 = 5 × 5) and (60 = 2 × 2 × 3 × 5). LCM of 25 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 25 and 60.
⇒ LCM of 25, 60 = 2^{2} × 3^{1} × 5^{2} = 300.
What is the Relation Between GCF and LCM of 25, 60?
The following equation can be used to express the relation between GCF and LCM of 25 and 60, i.e. GCF × LCM = 25 × 60.
What are the Methods to Find LCM of 25 and 60?
The commonly used methods to find the LCM of 25 and 60 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
If the LCM of 60 and 25 is 300, Find its GCF.
LCM(60, 25) × GCF(60, 25) = 60 × 25
Since the LCM of 60 and 25 = 300
⇒ 300 × GCF(60, 25) = 1500
Therefore, the greatest common factor (GCF) = 1500/300 = 5.
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