LCM of 36 and 63
LCM of 36 and 63 is the smallest number among all common multiples of 36 and 63. The first few multiples of 36 and 63 are (36, 72, 108, 144, . . . ) and (63, 126, 189, 252, 315, 378, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 63  by division method, by listing multiples, and by prime factorization.
1.  LCM of 36 and 63 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 36 and 63?
Answer: LCM of 36 and 63 is 252.
Explanation:
The LCM of two nonzero integers, x(36) and y(63), is the smallest positive integer m(252) that is divisible by both x(36) and y(63) without any remainder.
Methods to Find LCM of 36 and 63
The methods to find the LCM of 36 and 63 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 36 and 63 by Division Method
To calculate the LCM of 36 and 63 by the division method, we will divide the numbers(36, 63) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 63.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 63. Write this prime number(2) on the left of the given numbers(36 and 63), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (36, 63) 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 63 is the product of all prime numbers on the left, i.e. LCM(36, 63) by division method = 2 × 2 × 3 × 3 × 7 = 252.
LCM of 36 and 63 by Prime Factorization
Prime factorization of 36 and 63 is (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and (3 × 3 × 7) = 3^{2} × 7^{1} respectively. LCM of 36 and 63 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{2} × 7^{1} = 252.
Hence, the LCM of 36 and 63 by prime factorization is 252.
LCM of 36 and 63 by Listing Multiples
To calculate the LCM of 36 and 63 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, . . . ) and 63 (63, 126, 189, 252, 315, 378, . . . . )
 Step 2: The common multiples from the multiples of 36 and 63 are 252, 504, . . .
 Step 3: The smallest common multiple of 36 and 63 is 252.
∴ The least common multiple of 36 and 63 = 252.
☛ Also Check:
 LCM of 10, 25, 35 and 40  1400
 LCM of 24, 36 and 54  216
 LCM of 3 and 7  21
 LCM of 20 and 30  60
 LCM of 12 and 36  36
 LCM of 6, 8 and 15  120
 LCM of 9 and 21  63
LCM of 36 and 63 Examples

Example 1: Verify the relationship between GCF and LCM of 36 and 63.
Solution:
The relation between GCF and LCM of 36 and 63 is given as,
LCM(36, 63) × GCF(36, 63) = Product of 36, 63
Prime factorization of 36 and 63 is given as, 36 = (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and 63 = (3 × 3 × 7) = 3^{2} × 7^{1}
LCM(36, 63) = 252
GCF(36, 63) = 9
LHS = LCM(36, 63) × GCF(36, 63) = 252 × 9 = 2268
RHS = Product of 36, 63 = 36 × 63 = 2268
⇒ LHS = RHS = 2268
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 9 and 252 respectively. If one number is 36, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 36 × b
⇒ b = (GCD × LCM)/36
⇒ b = (9 × 252)/36
⇒ b = 63
Therefore, the other number is 63. 
Example 3: Find the smallest number that is divisible by 36 and 63 exactly.
Solution:
The smallest number that is divisible by 36 and 63 exactly is their LCM.
⇒ Multiples of 36 and 63: Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, . . . .
 Multiples of 63 = 63, 126, 189, 252, 315, 378, 441, . . . .
Therefore, the LCM of 36 and 63 is 252.
FAQs on LCM of 36 and 63
What is the LCM of 36 and 63?
The LCM of 36 and 63 is 252. To find the least common multiple (LCM) of 36 and 63, we need to find the multiples of 36 and 63 (multiples of 36 = 36, 72, 108, 144 . . . . 252; multiples of 63 = 63, 126, 189, 252) and choose the smallest multiple that is exactly divisible by 36 and 63, i.e., 252.
Which of the following is the LCM of 36 and 63? 252, 25, 42, 15
The value of LCM of 36, 63 is the smallest common multiple of 36 and 63. The number satisfying the given condition is 252.
If the LCM of 63 and 36 is 252, Find its GCF.
LCM(63, 36) × GCF(63, 36) = 63 × 36
Since the LCM of 63 and 36 = 252
⇒ 252 × GCF(63, 36) = 2268
Therefore, the greatest common factor (GCF) = 2268/252 = 9.
What are the Methods to Find LCM of 36 and 63?
The commonly used methods to find the LCM of 36 and 63 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
How to Find the LCM of 36 and 63 by Prime Factorization?
To find the LCM of 36 and 63 using prime factorization, we will find the prime factors, (36 = 2 × 2 × 3 × 3) and (63 = 3 × 3 × 7). LCM of 36 and 63 is the product of prime factors raised to their respective highest exponent among the numbers 36 and 63.
⇒ LCM of 36, 63 = 2^{2} × 3^{2} × 7^{1} = 252.