LCM of 8 and 64
LCM of 8 and 64 is the smallest number among all common multiples of 8 and 64. The first few multiples of 8 and 64 are (8, 16, 24, 32, 40, 48, 56, . . . ) and (64, 128, 192, 256, 320, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 64  by listing multiples, by prime factorization, and by division method.
1.  LCM of 8 and 64 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 8 and 64?
Answer: LCM of 8 and 64 is 64.
Explanation:
The LCM of two nonzero integers, x(8) and y(64), is the smallest positive integer m(64) that is divisible by both x(8) and y(64) without any remainder.
Methods to Find LCM of 8 and 64
Let's look at the different methods for finding the LCM of 8 and 64.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 8 and 64 by Division Method
To calculate the LCM of 8 and 64 by the division method, we will divide the numbers(8, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 64.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 64. Write this prime number(2) on the left of the given numbers(8 and 64), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (8, 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 8 and 64 is the product of all prime numbers on the left, i.e. LCM(8, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 = 64.
LCM of 8 and 64 by Listing Multiples
To calculate the LCM of 8 and 64 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 64 (64, 128, 192, 256, 320, . . . . )
 Step 2: The common multiples from the multiples of 8 and 64 are 64, 128, . . .
 Step 3: The smallest common multiple of 8 and 64 is 64.
∴ The least common multiple of 8 and 64 = 64.
LCM of 8 and 64 by Prime Factorization
Prime factorization of 8 and 64 is (2 × 2 × 2) = 2^{3} and (2 × 2 × 2 × 2 × 2 × 2) = 2^{6} respectively. LCM of 8 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{6} = 64.
Hence, the LCM of 8 and 64 by prime factorization is 64.
☛ Also Check:
 LCM of 24 and 8  24
 LCM of 12, 18 and 24  72
 LCM of 8, 9 and 12  72
 LCM of 8 and 12  24
 LCM of 8, 15 and 20  120
 LCM of 12, 18 and 20  180
 LCM of 7 and 28  28
LCM of 8 and 64 Examples

Example 1: Verify the relationship between GCF and LCM of 8 and 64.
Solution:
The relation between GCF and LCM of 8 and 64 is given as,
LCM(8, 64) × GCF(8, 64) = Product of 8, 64
Prime factorization of 8 and 64 is given as, 8 = (2 × 2 × 2) = 2^{3} and 64 = (2 × 2 × 2 × 2 × 2 × 2) = 2^{6}
LCM(8, 64) = 64
GCF(8, 64) = 8
LHS = LCM(8, 64) × GCF(8, 64) = 64 × 8 = 512
RHS = Product of 8, 64 = 8 × 64 = 512
⇒ LHS = RHS = 512
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 8 and 64 respectively. If one number is 8, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 8 × z
⇒ z = (GCD × LCM)/8
⇒ z = (8 × 64)/8
⇒ z = 64
Therefore, the other number is 64. 
Example 3: The product of two numbers is 512. If their GCD is 8, what is their LCM?
Solution:
Given: GCD = 8
product of numbers = 512
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 512/8
Therefore, the LCM is 64.
The probable combination for the given case is LCM(8, 64) = 64.
FAQs on LCM of 8 and 64
What is the LCM of 8 and 64?
The LCM of 8 and 64 is 64. To find the least common multiple of 8 and 64, we need to find the multiples of 8 and 64 (multiples of 8 = 8, 16, 24, 32 . . . . 64; multiples of 64 = 64, 128, 192, 256) and choose the smallest multiple that is exactly divisible by 8 and 64, i.e., 64.
How to Find the LCM of 8 and 64 by Prime Factorization?
To find the LCM of 8 and 64 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (64 = 2 × 2 × 2 × 2 × 2 × 2). LCM of 8 and 64 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 64.
⇒ LCM of 8, 64 = 2^{6} = 64.
What are the Methods to Find LCM of 8 and 64?
The commonly used methods to find the LCM of 8 and 64 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
If the LCM of 64 and 8 is 64, Find its GCF.
LCM(64, 8) × GCF(64, 8) = 64 × 8
Since the LCM of 64 and 8 = 64
⇒ 64 × GCF(64, 8) = 512
Therefore, the GCF (greatest common factor) = 512/64 = 8.
Which of the following is the LCM of 8 and 64? 30, 64, 40, 18
The value of LCM of 8, 64 is the smallest common multiple of 8 and 64. The number satisfying the given condition is 64.