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LCM of 4 and 28

LCM of 4 and 28 is the smallest number among all common multiples of 4 and 28. The first few multiples of 4 and 28 are (4, 8, 12, 16, 20, 24, . . . ) and (28, 56, 84, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 28 - by listing multiples, by prime factorization, and by division method.

1. LCM of 4 and 28
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 4 and 28?

Answer: LCM of 4 and 28 is 28.

LCM of 4 and 28

Explanation:

The LCM of two non-zero integers, x(4) and y(28), is the smallest positive integer m(28) that is divisible by both x(4) and y(28) without any remainder.

Methods to Find LCM of 4 and 28

Let's look at the different methods for finding the LCM of 4 and 28.

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

LCM of 4 and 28 by Listing Multiples

To calculate the LCM of 4 and 28 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 28 (28, 56, 84, 112, . . . . )
  • Step 2: The common multiples from the multiples of 4 and 28 are 28, 56, . . .
  • Step 3: The smallest common multiple of 4 and 28 is 28.

∴ The least common multiple of 4 and 28 = 28.

LCM of 4 and 28 by Prime Factorization

Prime factorization of 4 and 28 is (2 × 2) = 22 and (2 × 2 × 7) = 22 × 71 respectively. LCM of 4 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 71 = 28.
Hence, the LCM of 4 and 28 by prime factorization is 28.

LCM of 4 and 28 by Division Method

LCM of 4 and 28 by Division Method

To calculate the LCM of 4 and 28 by the division method, we will divide the numbers(4, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 28.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 28. Write this prime number(2) on the left of the given numbers(4 and 28), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (4, 28) 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 28 is the product of all prime numbers on the left, i.e. LCM(4, 28) by division method = 2 × 2 × 7 = 28.

☛ Also Check:

LCM of 4 and 28 Examples

  1. Example 1: The product of two numbers is 112. If their GCD is 4, what is their LCM?

    Solution:

    Given: GCD = 4
    product of numbers = 112
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 112/4
    Therefore, the LCM is 28.
    The probable combination for the given case is LCM(4, 28) = 28.

  2. Example 2: Verify the relationship between GCF and LCM of 4 and 28.

    Solution:

    The relation between GCF and LCM of 4 and 28 is given as,
    LCM(4, 28) × GCF(4, 28) = Product of 4, 28
    Prime factorization of 4 and 28 is given as, 4 = (2 × 2) = 22 and 28 = (2 × 2 × 7) = 22 × 71
    LCM(4, 28) = 28
    GCF(4, 28) = 4
    LHS = LCM(4, 28) × GCF(4, 28) = 28 × 4 = 112
    RHS = Product of 4, 28 = 4 × 28 = 112
    ⇒ LHS = RHS = 112
    Hence, verified.

  3. Example 3: The GCD and LCM of two numbers are 4 and 28 respectively. If one number is 28, find the other number.

    Solution:

    Let the other number be z.
    ∵ GCD × LCM = 28 × z
    ⇒ z = (GCD × LCM)/28
    ⇒ z = (4 × 28)/28
    ⇒ z = 4
    Therefore, the other number is 4.

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FAQs on LCM of 4 and 28

What is the LCM of 4 and 28?

The LCM of 4 and 28 is 28. To find the LCM of 4 and 28, we need to find the multiples of 4 and 28 (multiples of 4 = 4, 8, 12, 16 . . . . 28; multiples of 28 = 28, 56, 84, 112) and choose the smallest multiple that is exactly divisible by 4 and 28, i.e., 28.

Which of the following is the LCM of 4 and 28? 28, 18, 36, 20

The value of LCM of 4, 28 is the smallest common multiple of 4 and 28. The number satisfying the given condition is 28.

If the LCM of 28 and 4 is 28, Find its GCF.

LCM(28, 4) × GCF(28, 4) = 28 × 4
Since the LCM of 28 and 4 = 28
⇒ 28 × GCF(28, 4) = 112
Therefore, the greatest common factor = 112/28 = 4.

What are the Methods to Find LCM of 4 and 28?

The commonly used methods to find the LCM of 4 and 28 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples

What is the Relation Between GCF and LCM of 4, 28?

The following equation can be used to express the relation between GCF and LCM of 4 and 28, i.e. GCF × LCM = 4 × 28.

 
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