A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

LCM of 15 and 17

LCM of 15 and 17 is the smallest number among all common multiples of 15 and 17. The first few multiples of 15 and 17 are (15, 30, 45, 60, 75, . . . ) and (17, 34, 51, 68, 85, 102, 119, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 17 - by prime factorization, by listing multiples, and by division method.

1. LCM of 15 and 17
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 15 and 17?

Answer: LCM of 15 and 17 is 255.

LCM of 15 and 17

Explanation:

The LCM of two non-zero integers, x(15) and y(17), is the smallest positive integer m(255) that is divisible by both x(15) and y(17) without any remainder.

Methods to Find LCM of 15 and 17

The methods to find the LCM of 15 and 17 are explained below.

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

LCM of 15 and 17 by Listing Multiples

To calculate the LCM of 15 and 17 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, . . . ) and 17 (17, 34, 51, 68, 85, 102, 119, . . . . )
  • Step 2: The common multiples from the multiples of 15 and 17 are 255, 510, . . .
  • Step 3: The smallest common multiple of 15 and 17 is 255.

∴ The least common multiple of 15 and 17 = 255.

LCM of 15 and 17 by Prime Factorization

Prime factorization of 15 and 17 is (3 × 5) = 31 × 51 and (17) = 171 respectively. LCM of 15 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 31 × 51 × 171 = 255.
Hence, the LCM of 15 and 17 by prime factorization is 255.

LCM of 15 and 17 by Division Method

LCM of 15 and 17 by Division Method

To calculate the LCM of 15 and 17 by the division method, we will divide the numbers(15, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 17.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 17. Write this prime number(3) on the left of the given numbers(15 and 17), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (15, 17) is a multiple of 3, divide it by 3 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 17 is the product of all prime numbers on the left, i.e. LCM(15, 17) by division method = 3 × 5 × 17 = 255.

☛ Also Check:

LCM of 15 and 17 Examples

  1. Example 1: The product of two numbers is 255. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 255
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 255/1
    Therefore, the LCM is 255.
    The probable combination for the given case is LCM(15, 17) = 255.

  2. Example 2: Verify the relationship between GCF and LCM of 15 and 17.

    Solution:

    The relation between GCF and LCM of 15 and 17 is given as,
    LCM(15, 17) × GCF(15, 17) = Product of 15, 17
    Prime factorization of 15 and 17 is given as, 15 = (3 × 5) = 31 × 51 and 17 = (17) = 171
    LCM(15, 17) = 255
    GCF(15, 17) = 1
    LHS = LCM(15, 17) × GCF(15, 17) = 255 × 1 = 255
    RHS = Product of 15, 17 = 15 × 17 = 255
    ⇒ LHS = RHS = 255
    Hence, verified.

  3. Example 3: Find the smallest number that is divisible by 15 and 17 exactly.

    Solution:

    The value of LCM(15, 17) will be the smallest number that is exactly divisible by 15 and 17.
    ⇒ Multiples of 15 and 17:

    • Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 195, 210, 225, 240, 255, . . . .
    • Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, . . . ., 204, 221, 238, 255, . . . .

    Therefore, the LCM of 15 and 17 is 255.

Show Solution >

go to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

FAQs on LCM of 15 and 17

What is the LCM of 15 and 17?

The LCM of 15 and 17 is 255. To find the least common multiple of 15 and 17, we need to find the multiples of 15 and 17 (multiples of 15 = 15, 30, 45, 60 . . . . 255; multiples of 17 = 17, 34, 51, 68 . . . . 255) and choose the smallest multiple that is exactly divisible by 15 and 17, i.e., 255.

Which of the following is the LCM of 15 and 17? 255, 24, 42, 21

The value of LCM of 15, 17 is the smallest common multiple of 15 and 17. The number satisfying the given condition is 255.

What are the Methods to Find LCM of 15 and 17?

The commonly used methods to find the LCM of 15 and 17 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

What is the Relation Between GCF and LCM of 15, 17?

The following equation can be used to express the relation between GCF and LCM of 15 and 17, i.e. GCF × LCM = 15 × 17.

If the LCM of 17 and 15 is 255, Find its GCF.

LCM(17, 15) × GCF(17, 15) = 17 × 15
Since the LCM of 17 and 15 = 255
⇒ 255 × GCF(17, 15) = 255
Therefore, the GCF (greatest common factor) = 255/255 = 1.

 
Download FREE Study Materials
LCM and GCF
Math worksheets and
visual curriculum