LCM of 32 and 64
LCM of 32 and 64 is the smallest number among all common multiples of 32 and 64. The first few multiples of 32 and 64 are (32, 64, 96, 128, . . . ) and (64, 128, 192, 256, 320, 384, 448, . . . ) respectively. There are 3 commonly used methods to find LCM of 32 and 64  by division method, by listing multiples, and by prime factorization.
1.  LCM of 32 and 64 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 32 and 64?
Answer: LCM of 32 and 64 is 64.
Explanation:
The LCM of two nonzero integers, x(32) and y(64), is the smallest positive integer m(64) that is divisible by both x(32) and y(64) without any remainder.
Methods to Find LCM of 32 and 64
Let's look at the different methods for finding the LCM of 32 and 64.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 32 and 64 by Division Method
To calculate the LCM of 32 and 64 by the division method, we will divide the numbers(32, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 32 and 64.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 32 and 64. Write this prime number(2) on the left of the given numbers(32 and 64), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (32, 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 32 and 64 is the product of all prime numbers on the left, i.e. LCM(32, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 = 64.
LCM of 32 and 64 by Prime Factorization
Prime factorization of 32 and 64 is (2 × 2 × 2 × 2 × 2) = 2^{5} and (2 × 2 × 2 × 2 × 2 × 2) = 2^{6} respectively. LCM of 32 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{6} = 64.
Hence, the LCM of 32 and 64 by prime factorization is 64.
LCM of 32 and 64 by Listing Multiples
To calculate the LCM of 32 and 64 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 32 (32, 64, 96, 128, . . . ) and 64 (64, 128, 192, 256, 320, 384, 448, . . . . )
 Step 2: The common multiples from the multiples of 32 and 64 are 64, 128, . . .
 Step 3: The smallest common multiple of 32 and 64 is 64.
∴ The least common multiple of 32 and 64 = 64.
☛ Also Check:
 LCM of 36 and 40  360
 LCM of 40, 36 and 126  2520
 LCM of 45 and 75  225
 LCM of 15 and 40  120
 LCM of 15, 20 and 25  300
 LCM of 144 and 169  24336
 LCM of 11 and 22  22
LCM of 32 and 64 Examples

Example 1: The GCD and LCM of two numbers are 32 and 64 respectively. If one number is 32, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 32 × b
⇒ b = (GCD × LCM)/32
⇒ b = (32 × 64)/32
⇒ b = 64
Therefore, the other number is 64. 
Example 2: Find the smallest number that is divisible by 32 and 64 exactly.
Solution:
The smallest number that is divisible by 32 and 64 exactly is their LCM.
⇒ Multiples of 32 and 64: Multiples of 32 = 32, 64, 96, 128, 160, 192, . . . .
 Multiples of 64 = 64, 128, 192, 256, 320, 384, . . . .
Therefore, the LCM of 32 and 64 is 64.

Example 3: The product of two numbers is 2048. If their GCD is 32, what is their LCM?
Solution:
Given: GCD = 32
product of numbers = 2048
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2048/32
Therefore, the LCM is 64.
The probable combination for the given case is LCM(32, 64) = 64.
FAQs on LCM of 32 and 64
What is the LCM of 32 and 64?
The LCM of 32 and 64 is 64. To find the least common multiple (LCM) of 32 and 64, we need to find the multiples of 32 and 64 (multiples of 32 = 32, 64, 96, 128; multiples of 64 = 64, 128, 192, 256) and choose the smallest multiple that is exactly divisible by 32 and 64, i.e., 64.
What are the Methods to Find LCM of 32 and 64?
The commonly used methods to find the LCM of 32 and 64 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
What is the Relation Between GCF and LCM of 32, 64?
The following equation can be used to express the relation between GCF and LCM of 32 and 64, i.e. GCF × LCM = 32 × 64.
What is the Least Perfect Square Divisible by 32 and 64?
The least number divisible by 32 and 64 = LCM(32, 64)
LCM of 32 and 64 = 2 × 2 × 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 32 and 64 = 64 [Square root of 64 = √64 = ±8]
Therefore, 64 is the required number.
If the LCM of 64 and 32 is 64, Find its GCF.
LCM(64, 32) × GCF(64, 32) = 64 × 32
Since the LCM of 64 and 32 = 64
⇒ 64 × GCF(64, 32) = 2048
Therefore, the greatest common factor (GCF) = 2048/64 = 32.