A day full of math games & activities. Find one near you.

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 non-zero 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) = 2³ and (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ respectively. LCM of 8 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ = 64.
Hence, the LCM of 8 and 64 by prime factorization is 64.

☛ Also Check:

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) = 2³ and 64 = (2 × 2 × 2 × 2 × 2 × 2) = 2⁶
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.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

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 = 2⁶ = 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.

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum