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LCM of 15 and 35

LCM of 15 and 35 is the smallest number among all common multiples of 15 and 35. The first few multiples of 15 and 35 are (15, 30, 45, 60, 75, . . . ) and (35, 70, 105, 140, 175, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 35 - by prime factorization, by listing multiples, and by division method.

1. LCM of 15 and 35
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 15 and 35?

Answer: LCM of 15 and 35 is 105.

LCM of 15 and 35

Explanation:

The LCM of two non-zero integers, x(15) and y(35), is the smallest positive integer m(105) that is divisible by both x(15) and y(35) without any remainder.

Methods to Find LCM of 15 and 35

The methods to find the LCM of 15 and 35 are explained below.

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

LCM of 15 and 35 by Prime Factorization

Prime factorization of 15 and 35 is (3 × 5) = 31 × 51 and (5 × 7) = 51 × 71 respectively. LCM of 15 and 35 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 31 × 51 × 71 = 105.
Hence, the LCM of 15 and 35 by prime factorization is 105.

LCM of 15 and 35 by Listing Multiples

LCM of 15 and 35 by Listing Multiples Method

To calculate the LCM of 15 and 35 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 35 (35, 70, 105, 140, 175, 210, . . . . )
  • Step 2: The common multiples from the multiples of 15 and 35 are 105, 210, . . .
  • Step 3: The smallest common multiple of 15 and 35 is 105.

∴ The least common multiple of 15 and 35 = 105.

LCM of 15 and 35 by Division Method

To calculate the LCM of 15 and 35 by the division method, we will divide the numbers(15, 35) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 35.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 35. Write this prime number(3) on the left of the given numbers(15 and 35), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (15, 35) 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 35 is the product of all prime numbers on the left, i.e. LCM(15, 35) by division method = 3 × 5 × 7 = 105.

☛ Also Check:

LCM of 15 and 35 Examples

  1. Example 1: The product of two numbers is 525. If their GCD is 5, what is their LCM?

    Solution:

    Given: GCD = 5
    product of numbers = 525
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 525/5
    Therefore, the LCM is 105.
    The probable combination for the given case is LCM(15, 35) = 105.

  2. Example 2: Verify the relationship between GCF and LCM of 15 and 35.

    Solution:

    The relation between GCF and LCM of 15 and 35 is given as,
    LCM(15, 35) × GCF(15, 35) = Product of 15, 35
    Prime factorization of 15 and 35 is given as, 15 = (3 × 5) = 31 × 51 and 35 = (5 × 7) = 51 × 71
    LCM(15, 35) = 105
    GCF(15, 35) = 5
    LHS = LCM(15, 35) × GCF(15, 35) = 105 × 5 = 525
    RHS = Product of 15, 35 = 15 × 35 = 525
    ⇒ LHS = RHS = 525
    Hence, verified.

  3. Example 3: Find the smallest number that is divisible by 15 and 35 exactly.

    Solution:

    The smallest number that is divisible by 15 and 35 exactly is their LCM.
    ⇒ Multiples of 15 and 35:

    • Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, . . . .
    • Multiples of 35 = 35, 70, 105, 140, 175, 210, . . . .

    Therefore, the LCM of 15 and 35 is 105.

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FAQs on LCM of 15 and 35

What is the LCM of 15 and 35?

The LCM of 15 and 35 is 105. To find the least common multiple (LCM) of 15 and 35, we need to find the multiples of 15 and 35 (multiples of 15 = 15, 30, 45, 60 . . . . 105; multiples of 35 = 35, 70, 105, 140) and choose the smallest multiple that is exactly divisible by 15 and 35, i.e., 105.

How to Find the LCM of 15 and 35 by Prime Factorization?

To find the LCM of 15 and 35 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (35 = 5 × 7). LCM of 15 and 35 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 35.
⇒ LCM of 15, 35 = 31 × 51 × 71 = 105.

If the LCM of 35 and 15 is 105, Find its GCF.

LCM(35, 15) × GCF(35, 15) = 35 × 15
Since the LCM of 35 and 15 = 105
⇒ 105 × GCF(35, 15) = 525
Therefore, the greatest common factor (GCF) = 525/105 = 5.

What are the Methods to Find LCM of 15 and 35?

The commonly used methods to find the LCM of 15 and 35 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

Which of the following is the LCM of 15 and 35? 5, 36, 3, 105

The value of LCM of 15, 35 is the smallest common multiple of 15 and 35. The number satisfying the given condition is 105.

 
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