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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.

LCM of 8 and 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

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

  1. 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.

  2. 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.

  3. 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.

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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.

 
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