LCM of 36 and 45
LCM of 36 and 45 is the smallest number among all common multiples of 36 and 45. The first few multiples of 36 and 45 are (36, 72, 108, 144, 180, 216, . . . ) and (45, 90, 135, 180, 225, 270, 315, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 45  by prime factorization, by division method, and by listing multiples.
1.  LCM of 36 and 45 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 36 and 45?
Answer: LCM of 36 and 45 is 180.
Explanation:
The LCM of two nonzero integers, x(36) and y(45), is the smallest positive integer m(180) that is divisible by both x(36) and y(45) without any remainder.
Methods to Find LCM of 36 and 45
The methods to find the LCM of 36 and 45 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 36 and 45 by Prime Factorization
Prime factorization of 36 and 45 is (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and (3 × 3 × 5) = 3^{2} × 5^{1} respectively. LCM of 36 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{2} × 5^{1} = 180.
Hence, the LCM of 36 and 45 by prime factorization is 180.
LCM of 36 and 45 by Division Method
To calculate the LCM of 36 and 45 by the division method, we will divide the numbers(36, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 45.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 45. Write this prime number(2) on the left of the given numbers(36 and 45), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (36, 45) 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 36 and 45 is the product of all prime numbers on the left, i.e. LCM(36, 45) by division method = 2 × 2 × 3 × 3 × 5 = 180.
LCM of 36 and 45 by Listing Multiples
To calculate the LCM of 36 and 45 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 36 (36, 72, 108, 144, 180, 216, . . . ) and 45 (45, 90, 135, 180, 225, 270, 315, . . . . )
 Step 2: The common multiples from the multiples of 36 and 45 are 180, 360, . . .
 Step 3: The smallest common multiple of 36 and 45 is 180.
∴ The least common multiple of 36 and 45 = 180.
☛ Also Check:
 LCM of 21, 28, 36 and 45  1260
 LCM of 2, 5 and 7  70
 LCM of 144 and 180  720
 LCM of 45 and 90  90
 LCM of 4 and 7  28
 LCM of 18, 24 and 36  72
 LCM of 32 and 40  160
LCM of 36 and 45 Examples

Example 1: Find the smallest number that is divisible by 36 and 45 exactly.
Solution:
The smallest number that is divisible by 36 and 45 exactly is their LCM.
⇒ Multiples of 36 and 45: Multiples of 36 = 36, 72, 108, 144, 180, . . . .
 Multiples of 45 = 45, 90, 135, 180, 225, . . . .
Therefore, the LCM of 36 and 45 is 180.

Example 2: The product of two numbers is 1620. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 1620
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1620/9
Therefore, the LCM is 180.
The probable combination for the given case is LCM(36, 45) = 180. 
Example 3: The GCD and LCM of two numbers are 9 and 180 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 = (9 × 180)/36
⇒ a = 45
Therefore, the other number is 45.
FAQs on LCM of 36 and 45
What is the LCM of 36 and 45?
The LCM of 36 and 45 is 180. To find the LCM of 36 and 45, we need to find the multiples of 36 and 45 (multiples of 36 = 36, 72, 108, 144 . . . . 180; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 36 and 45, i.e., 180.
If the LCM of 45 and 36 is 180, Find its GCF.
LCM(45, 36) × GCF(45, 36) = 45 × 36
Since the LCM of 45 and 36 = 180
⇒ 180 × GCF(45, 36) = 1620
Therefore, the greatest common factor (GCF) = 1620/180 = 9.
What is the Least Perfect Square Divisible by 36 and 45?
The least number divisible by 36 and 45 = LCM(36, 45)
LCM of 36 and 45 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 36 and 45 = LCM(36, 45) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
Which of the following is the LCM of 36 and 45? 27, 5, 180, 16
The value of LCM of 36, 45 is the smallest common multiple of 36 and 45. The number satisfying the given condition is 180.
What is the Relation Between GCF and LCM of 36, 45?
The following equation can be used to express the relation between GCF and LCM of 36 and 45, i.e. GCF × LCM = 36 × 45.
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