LCM of 25 and 36
LCM of 25 and 36 is the smallest number among all common multiples of 25 and 36. The first few multiples of 25 and 36 are (25, 50, 75, 100, . . . ) and (36, 72, 108, 144, 180, 216, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 36  by listing multiples, by division method, and by prime factorization.
1.  LCM of 25 and 36 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 25 and 36?
Answer: LCM of 25 and 36 is 900.
Explanation:
The LCM of two nonzero integers, x(25) and y(36), is the smallest positive integer m(900) that is divisible by both x(25) and y(36) without any remainder.
Methods to Find LCM of 25 and 36
The methods to find the LCM of 25 and 36 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 25 and 36 by Prime Factorization
Prime factorization of 25 and 36 is (5 × 5) = 5^{2} and (2 × 2 × 3 × 3) = 2^{2} × 3^{2} respectively. LCM of 25 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{2} × 5^{2} = 900.
Hence, the LCM of 25 and 36 by prime factorization is 900.
LCM of 25 and 36 by Listing Multiples
To calculate the LCM of 25 and 36 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 36 (36, 72, 108, 144, 180, 216, . . . . )
 Step 2: The common multiples from the multiples of 25 and 36 are 900, 1800, . . .
 Step 3: The smallest common multiple of 25 and 36 is 900.
∴ The least common multiple of 25 and 36 = 900.
LCM of 25 and 36 by Division Method
To calculate the LCM of 25 and 36 by the division method, we will divide the numbers(25, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 36.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 36. Write this prime number(2) on the left of the given numbers(25 and 36), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (25, 36) 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 36 is the product of all prime numbers on the left, i.e. LCM(25, 36) by division method = 2 × 2 × 3 × 3 × 5 × 5 = 900.
☛ Also Check:
 LCM of 6 and 21  42
 LCM of 20 and 60  60
 LCM of 11 and 121  121
 LCM of 12 and 22  132
 LCM of 8 and 22  88
 LCM of 3, 5 and 7  105
 LCM of 60 and 700  2100
LCM of 25 and 36 Examples

Example 1: The GCD and LCM of two numbers are 1 and 900 respectively. If one number is 36, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 36 × a
⇒ a = (GCD × LCM)/36
⇒ a = (1 × 900)/36
⇒ a = 25
Therefore, the other number is 25. 
Example 2: Verify the relationship between GCF and LCM of 25 and 36.
Solution:
The relation between GCF and LCM of 25 and 36 is given as,
LCM(25, 36) × GCF(25, 36) = Product of 25, 36
Prime factorization of 25 and 36 is given as, 25 = (5 × 5) = 5^{2} and 36 = (2 × 2 × 3 × 3) = 2^{2} × 3^{2}
LCM(25, 36) = 900
GCF(25, 36) = 1
LHS = LCM(25, 36) × GCF(25, 36) = 900 × 1 = 900
RHS = Product of 25, 36 = 25 × 36 = 900
⇒ LHS = RHS = 900
Hence, verified. 
Example 3: Find the smallest number that is divisible by 25 and 36 exactly.
Solution:
The value of LCM(25, 36) will be the smallest number that is exactly divisible by 25 and 36.
⇒ Multiples of 25 and 36: Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 800, 825, 850, 875, 900, . . . .
 Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 828, 864, 900, . . . .
Therefore, the LCM of 25 and 36 is 900.
FAQs on LCM of 25 and 36
What is the LCM of 25 and 36?
The LCM of 25 and 36 is 900. To find the least common multiple (LCM) of 25 and 36, we need to find the multiples of 25 and 36 (multiples of 25 = 25, 50, 75, 100 . . . . 900; multiples of 36 = 36, 72, 108, 144 . . . . 900) and choose the smallest multiple that is exactly divisible by 25 and 36, i.e., 900.
How to Find the LCM of 25 and 36 by Prime Factorization?
To find the LCM of 25 and 36 using prime factorization, we will find the prime factors, (25 = 5 × 5) and (36 = 2 × 2 × 3 × 3). LCM of 25 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 25 and 36.
⇒ LCM of 25, 36 = 2^{2} × 3^{2} × 5^{2} = 900.
If the LCM of 36 and 25 is 900, Find its GCF.
LCM(36, 25) × GCF(36, 25) = 36 × 25
Since the LCM of 36 and 25 = 900
⇒ 900 × GCF(36, 25) = 900
Therefore, the GCF = 900/900 = 1.
What is the Relation Between GCF and LCM of 25, 36?
The following equation can be used to express the relation between GCF and LCM of 25 and 36, i.e. GCF × LCM = 25 × 36.
Which of the following is the LCM of 25 and 36? 32, 900, 30, 40
The value of LCM of 25, 36 is the smallest common multiple of 25 and 36. The number satisfying the given condition is 900.
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