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LCM of 15 and 28

LCM of 15 and 28 is the smallest number among all common multiples of 15 and 28. The first few multiples of 15 and 28 are (15, 30, 45, 60, 75, 90, . . . ) and (28, 56, 84, 112, 140, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 28 - by listing multiples, by division method, and by prime factorization.

1. LCM of 15 and 28
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 15 and 28?

Answer: LCM of 15 and 28 is 420.

LCM of 15 and 28

Explanation:

The LCM of two non-zero integers, x(15) and y(28), is the smallest positive integer m(420) that is divisible by both x(15) and y(28) without any remainder.

Methods to Find LCM of 15 and 28

The methods to find the LCM of 15 and 28 are explained below.

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

LCM of 15 and 28 by Division Method

LCM of 15 and 28 by Division Method

To calculate the LCM of 15 and 28 by the division method, we will divide the numbers(15, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 28.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 28. Write this prime number(2) on the left of the given numbers(15 and 28), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (15, 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 15 and 28 is the product of all prime numbers on the left, i.e. LCM(15, 28) by division method = 2 × 2 × 3 × 5 × 7 = 420.

LCM of 15 and 28 by Prime Factorization

Prime factorization of 15 and 28 is (3 × 5) = 31 × 51 and (2 × 2 × 7) = 22 × 71 respectively. LCM of 15 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 × 71 = 420.
Hence, the LCM of 15 and 28 by prime factorization is 420.

LCM of 15 and 28 by Listing Multiples

To calculate the LCM of 15 and 28 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, 90, . . . ) and 28 (28, 56, 84, 112, 140, . . . . )
  • Step 2: The common multiples from the multiples of 15 and 28 are 420, 840, . . .
  • Step 3: The smallest common multiple of 15 and 28 is 420.

∴ The least common multiple of 15 and 28 = 420.

☛ Also Check:

LCM of 15 and 28 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 15 and 28.

    Solution:

    The relation between GCF and LCM of 15 and 28 is given as,
    LCM(15, 28) × GCF(15, 28) = Product of 15, 28
    Prime factorization of 15 and 28 is given as, 15 = (3 × 5) = 31 × 51 and 28 = (2 × 2 × 7) = 22 × 71
    LCM(15, 28) = 420
    GCF(15, 28) = 1
    LHS = LCM(15, 28) × GCF(15, 28) = 420 × 1 = 420
    RHS = Product of 15, 28 = 15 × 28 = 420
    ⇒ LHS = RHS = 420
    Hence, verified.

  2. Example 2: Find the smallest number that is divisible by 15 and 28 exactly.

    Solution:

    The value of LCM(15, 28) will be the smallest number that is exactly divisible by 15 and 28.
    ⇒ Multiples of 15 and 28:

    • Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 375, 390, 405, 420, . . . .
    • Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, . . . ., 364, 392, 420, . . . .

    Therefore, the LCM of 15 and 28 is 420.

  3. Example 3: The GCD and LCM of two numbers are 1 and 420 respectively. If one number is 15, find the other number.

    Solution:

    Let the other number be m.
    ∵ GCD × LCM = 15 × m
    ⇒ m = (GCD × LCM)/15
    ⇒ m = (1 × 420)/15
    ⇒ m = 28
    Therefore, the other number is 28.

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FAQs on LCM of 15 and 28

What is the LCM of 15 and 28?

The LCM of 15 and 28 is 420. To find the LCM of 15 and 28, we need to find the multiples of 15 and 28 (multiples of 15 = 15, 30, 45, 60 . . . . 420; multiples of 28 = 28, 56, 84, 112 . . . . 420) and choose the smallest multiple that is exactly divisible by 15 and 28, i.e., 420.

Which of the following is the LCM of 15 and 28? 20, 420, 3, 42

The value of LCM of 15, 28 is the smallest common multiple of 15 and 28. The number satisfying the given condition is 420.

What is the Relation Between GCF and LCM of 15, 28?

The following equation can be used to express the relation between GCF and LCM of 15 and 28, i.e. GCF × LCM = 15 × 28.

What are the Methods to Find LCM of 15 and 28?

The commonly used methods to find the LCM of 15 and 28 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples

If the LCM of 28 and 15 is 420, Find its GCF.

LCM(28, 15) × GCF(28, 15) = 28 × 15
Since the LCM of 28 and 15 = 420
⇒ 420 × GCF(28, 15) = 420
Therefore, the greatest common factor (GCF) = 420/420 = 1.

 
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