LCM of 8 and 32
LCM of 8 and 32 is the smallest number among all common multiples of 8 and 32. The first few multiples of 8 and 32 are (8, 16, 24, 32, 40, 48, 56, . . . ) and (32, 64, 96, 128, 160, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 32  by division method, by prime factorization, and by listing multiples.
1.  LCM of 8 and 32 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 8 and 32?
Answer: LCM of 8 and 32 is 32.
Explanation:
The LCM of two nonzero integers, x(8) and y(32), is the smallest positive integer m(32) that is divisible by both x(8) and y(32) without any remainder.
Methods to Find LCM of 8 and 32
Let's look at the different methods for finding the LCM of 8 and 32.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 8 and 32 by Division Method
To calculate the LCM of 8 and 32 by the division method, we will divide the numbers(8, 32) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 32.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 32. Write this prime number(2) on the left of the given numbers(8 and 32), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (8, 32) 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 8 and 32 is the product of all prime numbers on the left, i.e. LCM(8, 32) by division method = 2 × 2 × 2 × 2 × 2 = 32.
LCM of 8 and 32 by Prime Factorization
Prime factorization of 8 and 32 is (2 × 2 × 2) = 2^{3} and (2 × 2 × 2 × 2 × 2) = 2^{5} respectively. LCM of 8 and 32 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{5} = 32.
Hence, the LCM of 8 and 32 by prime factorization is 32.
LCM of 8 and 32 by Listing Multiples
To calculate the LCM of 8 and 32 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, 56, . . . ) and 32 (32, 64, 96, 128, 160, . . . . )
 Step 2: The common multiples from the multiples of 8 and 32 are 32, 64, . . .
 Step 3: The smallest common multiple of 8 and 32 is 32.
∴ The least common multiple of 8 and 32 = 32.
☛ Also Check:
 LCM of 20 and 50  100
 LCM of 24, 36, 44 and 62  24552
 LCM of 72, 108 and 2100  37800
 LCM of 6 and 16  48
 LCM of 4 and 8  8
 LCM of 48 and 56  336
 LCM of 25 and 50  50
LCM of 8 and 32 Examples

Example 1: The product of two numbers is 256. If their GCD is 8, what is their LCM?
Solution:
Given: GCD = 8
product of numbers = 256
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 256/8
Therefore, the LCM is 32.
The probable combination for the given case is LCM(8, 32) = 32. 
Example 2: Verify the relationship between GCF and LCM of 8 and 32.
Solution:
The relation between GCF and LCM of 8 and 32 is given as,
LCM(8, 32) × GCF(8, 32) = Product of 8, 32
Prime factorization of 8 and 32 is given as, 8 = (2 × 2 × 2) = 2^{3} and 32 = (2 × 2 × 2 × 2 × 2) = 2^{5}
LCM(8, 32) = 32
GCF(8, 32) = 8
LHS = LCM(8, 32) × GCF(8, 32) = 32 × 8 = 256
RHS = Product of 8, 32 = 8 × 32 = 256
⇒ LHS = RHS = 256
Hence, verified. 
Example 3: Find the smallest number that is divisible by 8 and 32 exactly.
Solution:
The smallest number that is divisible by 8 and 32 exactly is their LCM.
⇒ Multiples of 8 and 32: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, . . . .
 Multiples of 32 = 32, 64, 96, 128, 160, 192, 224, . . . .
Therefore, the LCM of 8 and 32 is 32.
FAQs on LCM of 8 and 32
What is the LCM of 8 and 32?
The LCM of 8 and 32 is 32. To find the least common multiple of 8 and 32, we need to find the multiples of 8 and 32 (multiples of 8 = 8, 16, 24, 32; multiples of 32 = 32, 64, 96, 128) and choose the smallest multiple that is exactly divisible by 8 and 32, i.e., 32.
What is the Least Perfect Square Divisible by 8 and 32?
The least number divisible by 8 and 32 = LCM(8, 32)
LCM of 8 and 32 = 2 × 2 × 2 × 2 × 2 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 8 and 32 = LCM(8, 32) × 2 = 64 [Square root of 64 = √64 = ±8]
Therefore, 64 is the required number.
How to Find the LCM of 8 and 32 by Prime Factorization?
To find the LCM of 8 and 32 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (32 = 2 × 2 × 2 × 2 × 2). LCM of 8 and 32 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 32.
⇒ LCM of 8, 32 = 2^{5} = 32.
If the LCM of 32 and 8 is 32, Find its GCF.
LCM(32, 8) × GCF(32, 8) = 32 × 8
Since the LCM of 32 and 8 = 32
⇒ 32 × GCF(32, 8) = 256
Therefore, the GCF (greatest common factor) = 256/32 = 8.
What are the Methods to Find LCM of 8 and 32?
The commonly used methods to find the LCM of 8 and 32 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
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