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LCM of 7 and 49

LCM of 7 and 49 is the smallest number among all common multiples of 7 and 49. The first few multiples of 7 and 49 are (7, 14, 21, 28, 35, 42, . . . ) and (49, 98, 147, 196, 245, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 49 - by division method, by prime factorization, and by listing multiples.

1. LCM of 7 and 49
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 7 and 49?

Answer: LCM of 7 and 49 is 49.

LCM of 7 and 49

Explanation:

The LCM of two non-zero integers, x(7) and y(49), is the smallest positive integer m(49) that is divisible by both x(7) and y(49) without any remainder.

Methods to Find LCM of 7 and 49

The methods to find the LCM of 7 and 49 are explained below.

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

LCM of 7 and 49 by Listing Multiples

To calculate the LCM of 7 and 49 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, . . . ) and 49 (49, 98, 147, 196, 245, . . . . )
  • Step 2: The common multiples from the multiples of 7 and 49 are 49, 98, . . .
  • Step 3: The smallest common multiple of 7 and 49 is 49.

∴ The least common multiple of 7 and 49 = 49.

LCM of 7 and 49 by Division Method

LCM of 7 and 49 by Division Method

To calculate the LCM of 7 and 49 by the division method, we will divide the numbers(7, 49) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 49.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 49. Write this prime number(7) on the left of the given numbers(7 and 49), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (7, 49) is a multiple of 7, divide it by 7 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 7 and 49 is the product of all prime numbers on the left, i.e. LCM(7, 49) by division method = 7 × 7 = 49.

LCM of 7 and 49 by Prime Factorization

Prime factorization of 7 and 49 is (7) = 71 and (7 × 7) = 72 respectively. LCM of 7 and 49 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 72 = 49.
Hence, the LCM of 7 and 49 by prime factorization is 49.

☛ Also Check:

LCM of 7 and 49 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 7 and 49.

    Solution:

    The relation between GCF and LCM of 7 and 49 is given as,
    LCM(7, 49) × GCF(7, 49) = Product of 7, 49
    Prime factorization of 7 and 49 is given as, 7 = (7) = 71 and 49 = (7 × 7) = 72
    LCM(7, 49) = 49
    GCF(7, 49) = 7
    LHS = LCM(7, 49) × GCF(7, 49) = 49 × 7 = 343
    RHS = Product of 7, 49 = 7 × 49 = 343
    ⇒ LHS = RHS = 343
    Hence, verified.

  2. Example 2: The GCD and LCM of two numbers are 7 and 49 respectively. If one number is 49, find the other number.

    Solution:

    Let the other number be b.
    ∵ GCD × LCM = 49 × b
    ⇒ b = (GCD × LCM)/49
    ⇒ b = (7 × 49)/49
    ⇒ b = 7
    Therefore, the other number is 7.

  3. Example 3: The product of two numbers is 343. If their GCD is 7, what is their LCM?

    Solution:

    Given: GCD = 7
    product of numbers = 343
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 343/7
    Therefore, the LCM is 49.
    The probable combination for the given case is LCM(7, 49) = 49.

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FAQs on LCM of 7 and 49

What is the LCM of 7 and 49?

The LCM of 7 and 49 is 49. To find the LCM (least common multiple) of 7 and 49, we need to find the multiples of 7 and 49 (multiples of 7 = 7, 14, 21, 28 . . . . 49; multiples of 49 = 49, 98, 147, 196) and choose the smallest multiple that is exactly divisible by 7 and 49, i.e., 49.

What is the Relation Between GCF and LCM of 7, 49?

The following equation can be used to express the relation between GCF and LCM of 7 and 49, i.e. GCF × LCM = 7 × 49.

Which of the following is the LCM of 7 and 49? 12, 49, 32, 10

The value of LCM of 7, 49 is the smallest common multiple of 7 and 49. The number satisfying the given condition is 49.

What are the Methods to Find LCM of 7 and 49?

The commonly used methods to find the LCM of 7 and 49 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples

If the LCM of 49 and 7 is 49, Find its GCF.

LCM(49, 7) × GCF(49, 7) = 49 × 7
Since the LCM of 49 and 7 = 49
⇒ 49 × GCF(49, 7) = 343
Therefore, the greatest common factor = 343/49 = 7.

 
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