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 42 and 56

LCM of 42 and 56 is the smallest number among all common multiples of 42 and 56. The first few multiples of 42 and 56 are (42, 84, 126, 168, 210, 252, . . . ) and (56, 112, 168, 224, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 56 - by division method, by prime factorization, and by listing multiples.

1. LCM of 42 and 56
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 42 and 56?

Answer: LCM of 42 and 56 is 168.

LCM of 42 and 56

Explanation:

The LCM of two non-zero integers, x(42) and y(56), is the smallest positive integer m(168) that is divisible by both x(42) and y(56) without any remainder.

Methods to Find LCM of 42 and 56

The methods to find the LCM of 42 and 56 are explained below.

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

LCM of 42 and 56 by Prime Factorization

Prime factorization of 42 and 56 is (2 × 3 × 7) = 21 × 31 × 71 and (2 × 2 × 2 × 7) = 23 × 71 respectively. LCM of 42 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 71 = 168.
Hence, the LCM of 42 and 56 by prime factorization is 168.

LCM of 42 and 56 by Listing Multiples

LCM of 42 and 56 by Listing Multiples Method

To calculate the LCM of 42 and 56 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 42 (42, 84, 126, 168, 210, 252, . . . ) and 56 (56, 112, 168, 224, . . . . )
  • Step 2: The common multiples from the multiples of 42 and 56 are 168, 336, . . .
  • Step 3: The smallest common multiple of 42 and 56 is 168.

∴ The least common multiple of 42 and 56 = 168.

LCM of 42 and 56 by Division Method

To calculate the LCM of 42 and 56 by the division method, we will divide the numbers(42, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 56.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 56. Write this prime number(2) on the left of the given numbers(42 and 56), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (42, 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 42 and 56 is the product of all prime numbers on the left, i.e. LCM(42, 56) by division method = 2 × 2 × 2 × 3 × 7 = 168.

☛ Also Check:

LCM of 42 and 56 Examples

  1. Example 1: The GCD and LCM of two numbers are 14 and 168 respectively. If one number is 56, find the other number.

    Solution:

    Let the other number be z.
    ∵ GCD × LCM = 56 × z
    ⇒ z = (GCD × LCM)/56
    ⇒ z = (14 × 168)/56
    ⇒ z = 42
    Therefore, the other number is 42.

  2. Example 2: The product of two numbers is 2352. If their GCD is 14, what is their LCM?

    Solution:

    Given: GCD = 14
    product of numbers = 2352
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 2352/14
    Therefore, the LCM is 168.
    The probable combination for the given case is LCM(42, 56) = 168.

  3. Example 3: Verify the relationship between GCF and LCM of 42 and 56.

    Solution:

    The relation between GCF and LCM of 42 and 56 is given as,
    LCM(42, 56) × GCF(42, 56) = Product of 42, 56
    Prime factorization of 42 and 56 is given as, 42 = (2 × 3 × 7) = 21 × 31 × 71 and 56 = (2 × 2 × 2 × 7) = 23 × 71
    LCM(42, 56) = 168
    GCF(42, 56) = 14
    LHS = LCM(42, 56) × GCF(42, 56) = 168 × 14 = 2352
    RHS = Product of 42, 56 = 42 × 56 = 2352
    ⇒ LHS = RHS = 2352
    Hence, verified.

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 42 and 56

What is the LCM of 42 and 56?

The LCM of 42 and 56 is 168. To find the least common multiple of 42 and 56, we need to find the multiples of 42 and 56 (multiples of 42 = 42, 84, 126, 168; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 42 and 56, i.e., 168.

If the LCM of 56 and 42 is 168, Find its GCF.

LCM(56, 42) × GCF(56, 42) = 56 × 42
Since the LCM of 56 and 42 = 168
⇒ 168 × GCF(56, 42) = 2352
Therefore, the greatest common factor (GCF) = 2352/168 = 14.

What are the Methods to Find LCM of 42 and 56?

The commonly used methods to find the LCM of 42 and 56 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method

Which of the following is the LCM of 42 and 56? 168, 11, 45, 18

The value of LCM of 42, 56 is the smallest common multiple of 42 and 56. The number satisfying the given condition is 168.

What is the Relation Between GCF and LCM of 42, 56?

The following equation can be used to express the relation between GCF and LCM of 42 and 56, i.e. GCF × LCM = 42 × 56.

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