LCM of 63 and 81
LCM of 63 and 81 is the smallest number among all common multiples of 63 and 81. The first few multiples of 63 and 81 are (63, 126, 189, 252, 315, 378, 441, . . . ) and (81, 162, 243, 324, 405, 486, . . . ) respectively. There are 3 commonly used methods to find LCM of 63 and 81  by listing multiples, by prime factorization, and by division method.
1.  LCM of 63 and 81 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 63 and 81?
Answer: LCM of 63 and 81 is 567.
Explanation:
The LCM of two nonzero integers, x(63) and y(81), is the smallest positive integer m(567) that is divisible by both x(63) and y(81) without any remainder.
Methods to Find LCM of 63 and 81
Let's look at the different methods for finding the LCM of 63 and 81.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 63 and 81 by Listing Multiples
To calculate the LCM of 63 and 81 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 63 (63, 126, 189, 252, 315, 378, 441, . . . ) and 81 (81, 162, 243, 324, 405, 486, . . . . )
 Step 2: The common multiples from the multiples of 63 and 81 are 567, 1134, . . .
 Step 3: The smallest common multiple of 63 and 81 is 567.
∴ The least common multiple of 63 and 81 = 567.
LCM of 63 and 81 by Prime Factorization
Prime factorization of 63 and 81 is (3 × 3 × 7) = 3^{2} × 7^{1} and (3 × 3 × 3 × 3) = 3^{4} respectively. LCM of 63 and 81 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{4} × 7^{1} = 567.
Hence, the LCM of 63 and 81 by prime factorization is 567.
LCM of 63 and 81 by Division Method
To calculate the LCM of 63 and 81 by the division method, we will divide the numbers(63, 81) by their prime factors (preferably common). The product of these divisors gives the LCM of 63 and 81.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 63 and 81. Write this prime number(3) on the left of the given numbers(63 and 81), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (63, 81) is a multiple of 3, divide it by 3 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 63 and 81 is the product of all prime numbers on the left, i.e. LCM(63, 81) by division method = 3 × 3 × 3 × 3 × 7 = 567.
☛ Also Check:
 LCM of 5 and 20  20
 LCM of 7, 8 and 9  504
 LCM of 25 and 75  75
 LCM of 3, 8 and 12  24
 LCM of 3 and 1  3
 LCM of 5 and 11  55
 LCM of 9 and 11  99
LCM of 63 and 81 Examples

Example 1: The product of two numbers is 5103. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 5103
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 5103/9
Therefore, the LCM is 567.
The probable combination for the given case is LCM(63, 81) = 567. 
Example 2: The GCD and LCM of two numbers are 9 and 567 respectively. If one number is 81, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 81 × z
⇒ z = (GCD × LCM)/81
⇒ z = (9 × 567)/81
⇒ z = 63
Therefore, the other number is 63. 
Example 3: Find the smallest number that is divisible by 63 and 81 exactly.
Solution:
The smallest number that is divisible by 63 and 81 exactly is their LCM.
⇒ Multiples of 63 and 81: Multiples of 63 = 63, 126, 189, 252, 315, 378, 441, 504, 567, . . . .
 Multiples of 81 = 81, 162, 243, 324, 405, 486, 567, . . . .
Therefore, the LCM of 63 and 81 is 567.
FAQs on LCM of 63 and 81
What is the LCM of 63 and 81?
The LCM of 63 and 81 is 567. To find the least common multiple (LCM) of 63 and 81, we need to find the multiples of 63 and 81 (multiples of 63 = 63, 126, 189, 252 . . . . 567; multiples of 81 = 81, 162, 243, 324 . . . . 567) and choose the smallest multiple that is exactly divisible by 63 and 81, i.e., 567.
What is the Relation Between GCF and LCM of 63, 81?
The following equation can be used to express the relation between GCF and LCM of 63 and 81, i.e. GCF × LCM = 63 × 81.
If the LCM of 81 and 63 is 567, Find its GCF.
LCM(81, 63) × GCF(81, 63) = 81 × 63
Since the LCM of 81 and 63 = 567
⇒ 567 × GCF(81, 63) = 5103
Therefore, the greatest common factor (GCF) = 5103/567 = 9.
What is the Least Perfect Square Divisible by 63 and 81?
The least number divisible by 63 and 81 = LCM(63, 81)
LCM of 63 and 81 = 3 × 3 × 3 × 3 × 7 [Incomplete pair(s): 7]
⇒ Least perfect square divisible by each 63 and 81 = LCM(63, 81) × 7 = 3969 [Square root of 3969 = √3969 = ±63]
Therefore, 3969 is the required number.
Which of the following is the LCM of 63 and 81? 567, 18, 24, 3
The value of LCM of 63, 81 is the smallest common multiple of 63 and 81. The number satisfying the given condition is 567.
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