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LCM of 4 and 64

LCM of 4 and 64 is the smallest number among all common multiples of 4 and 64. The first few multiples of 4 and 64 are (4, 8, 12, 16, 20, 24, . . . ) and (64, 128, 192, 256, 320, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 64 - by listing multiples, by division method, and by prime factorization.

1. LCM of 4 and 64
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 4 and 64?

Answer: LCM of 4 and 64 is 64.

LCM of 4 and 64

Explanation:

The LCM of two non-zero integers, x(4) and y(64), is the smallest positive integer m(64) that is divisible by both x(4) and y(64) without any remainder.

Methods to Find LCM of 4 and 64

The methods to find the LCM of 4 and 64 are explained below.

  • By Listing Multiples
  • By Division Method
  • By Prime Factorization Method

LCM of 4 and 64 by Listing Multiples

To calculate the LCM of 4 and 64 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, . . . ) and 64 (64, 128, 192, 256, 320, . . . . )
  • Step 2: The common multiples from the multiples of 4 and 64 are 64, 128, . . .
  • Step 3: The smallest common multiple of 4 and 64 is 64.

∴ The least common multiple of 4 and 64 = 64.

LCM of 4 and 64 by Division Method

LCM of 4 and 64 by Division Method

To calculate the LCM of 4 and 64 by the division method, we will divide the numbers(4, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 64.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 64. Write this prime number(2) on the left of the given numbers(4 and 64), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (4, 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 4 and 64 is the product of all prime numbers on the left, i.e. LCM(4, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 = 64.

LCM of 4 and 64 by Prime Factorization

Prime factorization of 4 and 64 is (2 × 2) = 22 and (2 × 2 × 2 × 2 × 2 × 2) = 26 respectively. LCM of 4 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 26 = 64.
Hence, the LCM of 4 and 64 by prime factorization is 64.

☛ Also Check:

LCM of 4 and 64 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 4 and 64.

    Solution:

    The relation between GCF and LCM of 4 and 64 is given as,
    LCM(4, 64) × GCF(4, 64) = Product of 4, 64
    Prime factorization of 4 and 64 is given as, 4 = (2 × 2) = 22 and 64 = (2 × 2 × 2 × 2 × 2 × 2) = 26
    LCM(4, 64) = 64
    GCF(4, 64) = 4
    LHS = LCM(4, 64) × GCF(4, 64) = 64 × 4 = 256
    RHS = Product of 4, 64 = 4 × 64 = 256
    ⇒ LHS = RHS = 256
    Hence, verified.

  2. Example 2: Find the smallest number that is divisible by 4 and 64 exactly.

    Solution:

    The value of LCM(4, 64) will be the smallest number that is exactly divisible by 4 and 64.
    ⇒ Multiples of 4 and 64:

    • Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 56, 60, 64, . . . .
    • Multiples of 64 = 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, . . . ., -64, 0, 64, . . . .

    Therefore, the LCM of 4 and 64 is 64.

  3. Example 3: The product of two numbers is 256. If their GCD is 4, what is their LCM?

    Solution:

    Given: GCD = 4
    product of numbers = 256
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 256/4
    Therefore, the LCM is 64.
    The probable combination for the given case is LCM(4, 64) = 64.

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FAQs on LCM of 4 and 64

What is the LCM of 4 and 64?

The LCM of 4 and 64 is 64. To find the least common multiple (LCM) of 4 and 64, we need to find the multiples of 4 and 64 (multiples of 4 = 4, 8, 12, 16 . . . . 64; multiples of 64 = 64, 128, 192, 256) and choose the smallest multiple that is exactly divisible by 4 and 64, i.e., 64.

What is the Least Perfect Square Divisible by 4 and 64?

The least number divisible by 4 and 64 = LCM(4, 64)
LCM of 4 and 64 = 2 × 2 × 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 4 and 64 = 64 [Square root of 64 = √64 = ±8]
Therefore, 64 is the required number.

What are the Methods to Find LCM of 4 and 64?

The commonly used methods to find the LCM of 4 and 64 are:

  • Division Method
  • Listing Multiples
  • Prime Factorization Method

If the LCM of 64 and 4 is 64, Find its GCF.

LCM(64, 4) × GCF(64, 4) = 64 × 4
Since the LCM of 64 and 4 = 64
⇒ 64 × GCF(64, 4) = 256
Therefore, the greatest common factor (GCF) = 256/64 = 4.

What is the Relation Between GCF and LCM of 4, 64?

The following equation can be used to express the relation between GCF and LCM of 4 and 64, i.e. GCF × LCM = 4 × 64.

 
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