LCM of 10 and 25
LCM of 10 and 25 is the smallest number among all common multiples of 10 and 25. The first few multiples of 10 and 25 are (10, 20, 30, 40, 50, 60, . . . ) and (25, 50, 75, 100, 125, 150, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 25  by listing multiples, by division method, and by prime factorization.
1.  LCM of 10 and 25 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 10 and 25?
Answer: LCM of 10 and 25 is 50.
Explanation:
The LCM of two nonzero integers, x(10) and y(25), is the smallest positive integer m(50) that is divisible by both x(10) and y(25) without any remainder.
Methods to Find LCM of 10 and 25
Let's look at the different methods for finding the LCM of 10 and 25.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 10 and 25 by Prime Factorization
Prime factorization of 10 and 25 is (2 × 5) = 2^{1} × 5^{1} and (5 × 5) = 5^{2} respectively. LCM of 10 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 5^{2} = 50.
Hence, the LCM of 10 and 25 by prime factorization is 50.
LCM of 10 and 25 by Division Method
To calculate the LCM of 10 and 25 by the division method, we will divide the numbers(10, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 25.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 25. Write this prime number(2) on the left of the given numbers(10 and 25), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (10, 25) 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 10 and 25 is the product of all prime numbers on the left, i.e. LCM(10, 25) by division method = 2 × 5 × 5 = 50.
LCM of 10 and 25 by Listing Multiples
To calculate the LCM of 10 and 25 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, . . . ) and 25 (25, 50, 75, 100, 125, 150, . . . . )
 Step 2: The common multiples from the multiples of 10 and 25 are 50, 100, . . .
 Step 3: The smallest common multiple of 10 and 25 is 50.
∴ The least common multiple of 10 and 25 = 50.
☛ Also Check:
 LCM of 6 and 12  12
 LCM of 6 and 11  66
 LCM of 6 and 10  30
 LCM of 56 and 98  392
 LCM of 56 and 84  168
 LCM of 56 and 72  504
 LCM of 56 and 70  280
LCM of 10 and 25 Examples

Example 1: Verify the relationship between GCF and LCM of 10 and 25.
Solution:
The relation between GCF and LCM of 10 and 25 is given as,
LCM(10, 25) × GCF(10, 25) = Product of 10, 25
Prime factorization of 10 and 25 is given as, 10 = (2 × 5) = 2^{1} × 5^{1} and 25 = (5 × 5) = 5^{2}
LCM(10, 25) = 50
GCF(10, 25) = 5
LHS = LCM(10, 25) × GCF(10, 25) = 50 × 5 = 250
RHS = Product of 10, 25 = 10 × 25 = 250
⇒ LHS = RHS = 250
Hence, verified. 
Example 2: Find the smallest number that is divisible by 10 and 25 exactly.
Solution:
The smallest number that is divisible by 10 and 25 exactly is their LCM.
⇒ Multiples of 10 and 25: Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, . . . .
 Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, . . . .
Therefore, the LCM of 10 and 25 is 50.

Example 3: The GCD and LCM of two numbers are 5 and 50 respectively. If one number is 10, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 10 × p
⇒ p = (GCD × LCM)/10
⇒ p = (5 × 50)/10
⇒ p = 25
Therefore, the other number is 25.
FAQs on LCM of 10 and 25
What is the LCM of 10 and 25?
The LCM of 10 and 25 is 50. To find the LCM (least common multiple) of 10 and 25, we need to find the multiples of 10 and 25 (multiples of 10 = 10, 20, 30, 40 . . . . 50; multiples of 25 = 25, 50, 75, 100) and choose the smallest multiple that is exactly divisible by 10 and 25, i.e., 50.
What are the Methods to Find LCM of 10 and 25?
The commonly used methods to find the LCM of 10 and 25 are:
 Prime Factorization Method
 Listing Multiples
 Division Method
Which of the following is the LCM of 10 and 25? 50, 12, 21, 10
The value of LCM of 10, 25 is the smallest common multiple of 10 and 25. The number satisfying the given condition is 50.
What is the Relation Between GCF and LCM of 10, 25?
The following equation can be used to express the relation between GCF and LCM of 10 and 25, i.e. GCF × LCM = 10 × 25.
If the LCM of 25 and 10 is 50, Find its GCF.
LCM(25, 10) × GCF(25, 10) = 25 × 10
Since the LCM of 25 and 10 = 50
⇒ 50 × GCF(25, 10) = 250
Therefore, the GCF (greatest common factor) = 250/50 = 5.