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 35 and 56

LCM of 35 and 56 is the smallest number among all common multiples of 35 and 56. The first few multiples of 35 and 56 are (35, 70, 105, 140, 175, . . . ) and (56, 112, 168, 224, 280, 336, 392, . . . ) respectively. There are 3 commonly used methods to find LCM of 35 and 56 - by listing multiples, by prime factorization, and by division method.

1. LCM of 35 and 56
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 35 and 56?

Answer: LCM of 35 and 56 is 280.

LCM of 35 and 56

Explanation:

The LCM of two non-zero integers, x(35) and y(56), is the smallest positive integer m(280) that is divisible by both x(35) and y(56) without any remainder.

Methods to Find LCM of 35 and 56

Let's look at the different methods for finding the LCM of 35 and 56.

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

LCM of 35 and 56 by Listing Multiples

To calculate the LCM of 35 and 56 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 35 (35, 70, 105, 140, 175, . . . ) and 56 (56, 112, 168, 224, 280, 336, 392, . . . . )
  • Step 2: The common multiples from the multiples of 35 and 56 are 280, 560, . . .
  • Step 3: The smallest common multiple of 35 and 56 is 280.

∴ The least common multiple of 35 and 56 = 280.

LCM of 35 and 56 by Prime Factorization

Prime factorization of 35 and 56 is (5 × 7) = 51 × 71 and (2 × 2 × 2 × 7) = 23 × 71 respectively. LCM of 35 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 51 × 71 = 280.
Hence, the LCM of 35 and 56 by prime factorization is 280.

LCM of 35 and 56 by Division Method

LCM of 35 and 56 by Division Method

To calculate the LCM of 35 and 56 by the division method, we will divide the numbers(35, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 35 and 56.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 35 and 56. Write this prime number(2) on the left of the given numbers(35 and 56), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (35, 56) 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 35 and 56 is the product of all prime numbers on the left, i.e. LCM(35, 56) by division method = 2 × 2 × 2 × 5 × 7 = 280.

☛ Also Check:

LCM of 35 and 56 Examples

  1. Example 1: The GCD and LCM of two numbers are 7 and 280 respectively. If one number is 35, find the other number.

    Solution:

    Let the other number be p.
    ∵ GCD × LCM = 35 × p
    ⇒ p = (GCD × LCM)/35
    ⇒ p = (7 × 280)/35
    ⇒ p = 56
    Therefore, the other number is 56.

  2. Example 2: Verify the relationship between GCF and LCM of 35 and 56.

    Solution:

    The relation between GCF and LCM of 35 and 56 is given as,
    LCM(35, 56) × GCF(35, 56) = Product of 35, 56
    Prime factorization of 35 and 56 is given as, 35 = (5 × 7) = 51 × 71 and 56 = (2 × 2 × 2 × 7) = 23 × 71
    LCM(35, 56) = 280
    GCF(35, 56) = 7
    LHS = LCM(35, 56) × GCF(35, 56) = 280 × 7 = 1960
    RHS = Product of 35, 56 = 35 × 56 = 1960
    ⇒ LHS = RHS = 1960
    Hence, verified.

  3. Example 3: The product of two numbers is 1960. If their GCD is 7, what is their LCM?

    Solution:

    Given: GCD = 7
    product of numbers = 1960
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 1960/7
    Therefore, the LCM is 280.
    The probable combination for the given case is LCM(35, 56) = 280.

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 35 and 56

What is the LCM of 35 and 56?

The LCM of 35 and 56 is 280. To find the LCM of 35 and 56, we need to find the multiples of 35 and 56 (multiples of 35 = 35, 70, 105, 140 . . . . 280; multiples of 56 = 56, 112, 168, 224 . . . . 280) and choose the smallest multiple that is exactly divisible by 35 and 56, i.e., 280.

How to Find the LCM of 35 and 56 by Prime Factorization?

To find the LCM of 35 and 56 using prime factorization, we will find the prime factors, (35 = 5 × 7) and (56 = 2 × 2 × 2 × 7). LCM of 35 and 56 is the product of prime factors raised to their respective highest exponent among the numbers 35 and 56.
⇒ LCM of 35, 56 = 23 × 51 × 71 = 280.

If the LCM of 56 and 35 is 280, Find its GCF.

LCM(56, 35) × GCF(56, 35) = 56 × 35
Since the LCM of 56 and 35 = 280
⇒ 280 × GCF(56, 35) = 1960
Therefore, the greatest common factor (GCF) = 1960/280 = 7.

What are the Methods to Find LCM of 35 and 56?

The commonly used methods to find the LCM of 35 and 56 are:

  • Listing Multiples
  • Division Method
  • Prime Factorization Method

What is the Relation Between GCF and LCM of 35, 56?

The following equation can be used to express the relation between GCF and LCM of 35 and 56, i.e. GCF × LCM = 35 × 56.

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