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LCM of 28 and 98

LCM of 28 and 98 is the smallest number among all common multiples of 28 and 98. The first few multiples of 28 and 98 are (28, 56, 84, 112, 140, 168, 196, . . . ) and (98, 196, 294, 392, 490, 588, 686, . . . ) respectively. There are 3 commonly used methods to find LCM of 28 and 98 - by division method, by prime factorization, and by listing multiples.

1. LCM of 28 and 98
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 28 and 98?

Answer: LCM of 28 and 98 is 196.

LCM of 28 and 98

Explanation:

The LCM of two non-zero integers, x(28) and y(98), is the smallest positive integer m(196) that is divisible by both x(28) and y(98) without any remainder.

Methods to Find LCM of 28 and 98

The methods to find the LCM of 28 and 98 are explained below.

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

LCM of 28 and 98 by Prime Factorization

Prime factorization of 28 and 98 is (2 × 2 × 7) = 22 × 71 and (2 × 7 × 7) = 21 × 72 respectively. LCM of 28 and 98 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 72 = 196.
Hence, the LCM of 28 and 98 by prime factorization is 196.

LCM of 28 and 98 by Division Method

LCM of 28 and 98 by Division Method

To calculate the LCM of 28 and 98 by the division method, we will divide the numbers(28, 98) by their prime factors (preferably common). The product of these divisors gives the LCM of 28 and 98.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 28 and 98. Write this prime number(2) on the left of the given numbers(28 and 98), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (28, 98) 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 28 and 98 is the product of all prime numbers on the left, i.e. LCM(28, 98) by division method = 2 × 2 × 7 × 7 = 196.

LCM of 28 and 98 by Listing Multiples

To calculate the LCM of 28 and 98 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 28 (28, 56, 84, 112, 140, 168, 196, . . . ) and 98 (98, 196, 294, 392, 490, 588, 686, . . . . )
  • Step 2: The common multiples from the multiples of 28 and 98 are 196, 392, . . .
  • Step 3: The smallest common multiple of 28 and 98 is 196.

∴ The least common multiple of 28 and 98 = 196.

☛ Also Check:

LCM of 28 and 98 Examples

  1. Example 1: The GCD and LCM of two numbers are 14 and 196 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 = (14 × 196)/28
    ⇒ z = 98
    Therefore, the other number is 98.

  2. Example 2: Verify the relationship between GCF and LCM of 28 and 98.

    Solution:

    The relation between GCF and LCM of 28 and 98 is given as,
    LCM(28, 98) × GCF(28, 98) = Product of 28, 98
    Prime factorization of 28 and 98 is given as, 28 = (2 × 2 × 7) = 22 × 71 and 98 = (2 × 7 × 7) = 21 × 72
    LCM(28, 98) = 196
    GCF(28, 98) = 14
    LHS = LCM(28, 98) × GCF(28, 98) = 196 × 14 = 2744
    RHS = Product of 28, 98 = 28 × 98 = 2744
    ⇒ LHS = RHS = 2744
    Hence, verified.

  3. Example 3: Find the smallest number that is divisible by 28 and 98 exactly.

    Solution:

    The smallest number that is divisible by 28 and 98 exactly is their LCM.
    ⇒ Multiples of 28 and 98:

    • Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, . . . .
    • Multiples of 98 = 98, 196, 294, 392, 490, 588, . . . .

    Therefore, the LCM of 28 and 98 is 196.

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FAQs on LCM of 28 and 98

What is the LCM of 28 and 98?

The LCM of 28 and 98 is 196. To find the least common multiple (LCM) of 28 and 98, we need to find the multiples of 28 and 98 (multiples of 28 = 28, 56, 84, 112 . . . . 196; multiples of 98 = 98, 196, 294, 392) and choose the smallest multiple that is exactly divisible by 28 and 98, i.e., 196.

Which of the following is the LCM of 28 and 98? 196, 42, 30, 11

The value of LCM of 28, 98 is the smallest common multiple of 28 and 98. The number satisfying the given condition is 196.

If the LCM of 98 and 28 is 196, Find its GCF.

LCM(98, 28) × GCF(98, 28) = 98 × 28
Since the LCM of 98 and 28 = 196
⇒ 196 × GCF(98, 28) = 2744
Therefore, the greatest common factor = 2744/196 = 14.

What are the Methods to Find LCM of 28 and 98?

The commonly used methods to find the LCM of 28 and 98 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

What is the Relation Between GCF and LCM of 28, 98?

The following equation can be used to express the relation between GCF and LCM of 28 and 98, i.e. GCF × LCM = 28 × 98.

 
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