LCM of 36 and 81
LCM of 36 and 81 is the smallest number among all common multiples of 36 and 81. The first few multiples of 36 and 81 are (36, 72, 108, 144, 180, 216, . . . ) and (81, 162, 243, 324, 405, 486, 567, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 81  by prime factorization, by listing multiples, and by division method.
1.  LCM of 36 and 81 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 36 and 81?
Answer: LCM of 36 and 81 is 324.
Explanation:
The LCM of two nonzero integers, x(36) and y(81), is the smallest positive integer m(324) that is divisible by both x(36) and y(81) without any remainder.
Methods to Find LCM of 36 and 81
Let's look at the different methods for finding the LCM of 36 and 81.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 36 and 81 by Prime Factorization
Prime factorization of 36 and 81 is (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and (3 × 3 × 3 × 3) = 3^{4} respectively. LCM of 36 and 81 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{4} = 324.
Hence, the LCM of 36 and 81 by prime factorization is 324.
LCM of 36 and 81 by Listing Multiples
To calculate the LCM of 36 and 81 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 81 (81, 162, 243, 324, 405, 486, 567, . . . . )
 Step 2: The common multiples from the multiples of 36 and 81 are 324, 648, . . .
 Step 3: The smallest common multiple of 36 and 81 is 324.
∴ The least common multiple of 36 and 81 = 324.
LCM of 36 and 81 by Division Method
To calculate the LCM of 36 and 81 by the division method, we will divide the numbers(36, 81) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 81.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 81. Write this prime number(2) on the left of the given numbers(36 and 81), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (36, 81) 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 81 is the product of all prime numbers on the left, i.e. LCM(36, 81) by division method = 2 × 2 × 3 × 3 × 3 × 3 = 324.
☛ Also Check:
 LCM of 3, 6 and 8  24
 LCM of 24 and 60  120
 LCM of 42 and 63  126
 LCM of 18 and 45  90
 LCM of 8 and 11  88
 LCM of 30 and 75  150
 LCM of 5 and 12  60
LCM of 36 and 81 Examples

Example 1: Find the smallest number that is divisible by 36 and 81 exactly.
Solution:
The smallest number that is divisible by 36 and 81 exactly is their LCM.
⇒ Multiples of 36 and 81: Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, . . . .
 Multiples of 81 = 81, 162, 243, 324, 405, 486, . . . .
Therefore, the LCM of 36 and 81 is 324.

Example 2: Verify the relationship between GCF and LCM of 36 and 81.
Solution:
The relation between GCF and LCM of 36 and 81 is given as,
LCM(36, 81) × GCF(36, 81) = Product of 36, 81
Prime factorization of 36 and 81 is given as, 36 = (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and 81 = (3 × 3 × 3 × 3) = 3^{4}
LCM(36, 81) = 324
GCF(36, 81) = 9
LHS = LCM(36, 81) × GCF(36, 81) = 324 × 9 = 2916
RHS = Product of 36, 81 = 36 × 81 = 2916
⇒ LHS = RHS = 2916
Hence, verified. 
Example 3: The GCD and LCM of two numbers are 9 and 324 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 × 324)/36
⇒ a = 81
Therefore, the other number is 81.
FAQs on LCM of 36 and 81
What is the LCM of 36 and 81?
The LCM of 36 and 81 is 324. To find the least common multiple of 36 and 81, we need to find the multiples of 36 and 81 (multiples of 36 = 36, 72, 108, 144 . . . . 324; multiples of 81 = 81, 162, 243, 324) and choose the smallest multiple that is exactly divisible by 36 and 81, i.e., 324.
If the LCM of 81 and 36 is 324, Find its GCF.
LCM(81, 36) × GCF(81, 36) = 81 × 36
Since the LCM of 81 and 36 = 324
⇒ 324 × GCF(81, 36) = 2916
Therefore, the greatest common factor (GCF) = 2916/324 = 9.
What is the Relation Between GCF and LCM of 36, 81?
The following equation can be used to express the relation between GCF and LCM of 36 and 81, i.e. GCF × LCM = 36 × 81.
What is the Least Perfect Square Divisible by 36 and 81?
The least number divisible by 36 and 81 = LCM(36, 81)
LCM of 36 and 81 = 2 × 2 × 3 × 3 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 36 and 81 = 324 [Square root of 324 = √324 = ±18]
Therefore, 324 is the required number.
Which of the following is the LCM of 36 and 81? 21, 324, 10, 18
The value of LCM of 36, 81 is the smallest common multiple of 36 and 81. The number satisfying the given condition is 324.