LCM of 36 and 64
LCM of 36 and 64 is the smallest number among all common multiples of 36 and 64. The first few multiples of 36 and 64 are (36, 72, 108, 144, . . . ) and (64, 128, 192, 256, 320, 384, 448, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 64  by listing multiples, by division method, and by prime factorization.
1.  LCM of 36 and 64 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 36 and 64?
Answer: LCM of 36 and 64 is 576.
Explanation:
The LCM of two nonzero integers, x(36) and y(64), is the smallest positive integer m(576) that is divisible by both x(36) and y(64) without any remainder.
Methods to Find LCM of 36 and 64
Let's look at the different methods for finding the LCM of 36 and 64.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 36 and 64 by Prime Factorization
Prime factorization of 36 and 64 is (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and (2 × 2 × 2 × 2 × 2 × 2) = 2^{6} respectively. LCM of 36 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{6} × 3^{2} = 576.
Hence, the LCM of 36 and 64 by prime factorization is 576.
LCM of 36 and 64 by Listing Multiples
To calculate the LCM of 36 and 64 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 64 (64, 128, 192, 256, 320, 384, 448, . . . . )
 Step 2: The common multiples from the multiples of 36 and 64 are 576, 1152, . . .
 Step 3: The smallest common multiple of 36 and 64 is 576.
∴ The least common multiple of 36 and 64 = 576.
LCM of 36 and 64 by Division Method
To calculate the LCM of 36 and 64 by the division method, we will divide the numbers(36, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 64.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 64. Write this prime number(2) on the left of the given numbers(36 and 64), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (36, 64) 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 64 is the product of all prime numbers on the left, i.e. LCM(36, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 = 576.
☛ Also Check:
 LCM of 10 and 16  80
 LCM of 14 and 56  56
 LCM of 18 and 17  306
 LCM of 14 and 49  98
 LCM of 10 and 25  50
 LCM of 8 and 36  72
 LCM of 24 and 56  168
LCM of 36 and 64 Examples

Example 1: Verify the relationship between GCF and LCM of 36 and 64.
Solution:
The relation between GCF and LCM of 36 and 64 is given as,
LCM(36, 64) × GCF(36, 64) = Product of 36, 64
Prime factorization of 36 and 64 is given as, 36 = (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and 64 = (2 × 2 × 2 × 2 × 2 × 2) = 2^{6}
LCM(36, 64) = 576
GCF(36, 64) = 4
LHS = LCM(36, 64) × GCF(36, 64) = 576 × 4 = 2304
RHS = Product of 36, 64 = 36 × 64 = 2304
⇒ LHS = RHS = 2304
Hence, verified. 
Example 2: The product of two numbers is 2304. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 2304
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2304/4
Therefore, the LCM is 576.
The probable combination for the given case is LCM(36, 64) = 576. 
Example 3: Find the smallest number that is divisible by 36 and 64 exactly.
Solution:
The value of LCM(36, 64) will be the smallest number that is exactly divisible by 36 and 64.
⇒ Multiples of 36 and 64: Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 468, 504, 540, 576, . . . .
 Multiples of 64 = 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, . . . ., 384, 448, 512, 576, . . . .
Therefore, the LCM of 36 and 64 is 576.
FAQs on LCM of 36 and 64
What is the LCM of 36 and 64?
The LCM of 36 and 64 is 576. To find the least common multiple (LCM) of 36 and 64, we need to find the multiples of 36 and 64 (multiples of 36 = 36, 72, 108, 144 . . . . 576; multiples of 64 = 64, 128, 192, 256 . . . . 576) and choose the smallest multiple that is exactly divisible by 36 and 64, i.e., 576.
What are the Methods to Find LCM of 36 and 64?
The commonly used methods to find the LCM of 36 and 64 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
If the LCM of 64 and 36 is 576, Find its GCF.
LCM(64, 36) × GCF(64, 36) = 64 × 36
Since the LCM of 64 and 36 = 576
⇒ 576 × GCF(64, 36) = 2304
Therefore, the greatest common factor (GCF) = 2304/576 = 4.
Which of the following is the LCM of 36 and 64? 576, 30, 50, 21
The value of LCM of 36, 64 is the smallest common multiple of 36 and 64. The number satisfying the given condition is 576.
What is the Least Perfect Square Divisible by 36 and 64?
The least number divisible by 36 and 64 = LCM(36, 64)
LCM of 36 and 64 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 36 and 64 = 576 [Square root of 576 = √576 = ±24]
Therefore, 576 is the required number.
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