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LCM of 35 and 49

LCM of 35 and 49 is the smallest number among all common multiples of 35 and 49. The first few multiples of 35 and 49 are (35, 70, 105, 140, 175, . . . ) and (49, 98, 147, 196, 245, 294, 343, . . . ) respectively. There are 3 commonly used methods to find LCM of 35 and 49 - by listing multiples, by prime factorization, and by division method.

1. LCM of 35 and 49
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 35 and 49?

Answer: LCM of 35 and 49 is 245.

LCM of 35 and 49

Explanation:

The LCM of two non-zero integers, x(35) and y(49), is the smallest positive integer m(245) that is divisible by both x(35) and y(49) without any remainder.

Methods to Find LCM of 35 and 49

Let's look at the different methods for finding the LCM of 35 and 49.

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

LCM of 35 and 49 by Listing Multiples

To calculate the LCM of 35 and 49 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 49 (49, 98, 147, 196, 245, 294, 343, . . . . )
  • Step 2: The common multiples from the multiples of 35 and 49 are 245, 490, . . .
  • Step 3: The smallest common multiple of 35 and 49 is 245.

∴ The least common multiple of 35 and 49 = 245.

LCM of 35 and 49 by Prime Factorization

Prime factorization of 35 and 49 is (5 × 7) = 51 × 71 and (7 × 7) = 72 respectively. LCM of 35 and 49 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 51 × 72 = 245.
Hence, the LCM of 35 and 49 by prime factorization is 245.

LCM of 35 and 49 by Division Method

LCM of 35 and 49 by Division Method

To calculate the LCM of 35 and 49 by the division method, we will divide the numbers(35, 49) by their prime factors (preferably common). The product of these divisors gives the LCM of 35 and 49.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 35 and 49. Write this prime number(5) on the left of the given numbers(35 and 49), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (35, 49) is a multiple of 5, divide it by 5 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 49 is the product of all prime numbers on the left, i.e. LCM(35, 49) by division method = 5 × 7 × 7 = 245.

☛ Also Check:

LCM of 35 and 49 Examples

  1. Example 1: Find the smallest number that is divisible by 35 and 49 exactly.

    Solution:

    The smallest number that is divisible by 35 and 49 exactly is their LCM.
    ⇒ Multiples of 35 and 49:

    • Multiples of 35 = 35, 70, 105, 140, 175, 210, 245, . . . .
    • Multiples of 49 = 49, 98, 147, 196, 245, 294, 343, . . . .

    Therefore, the LCM of 35 and 49 is 245.

  2. Example 2: Verify the relationship between GCF and LCM of 35 and 49.

    Solution:

    The relation between GCF and LCM of 35 and 49 is given as,
    LCM(35, 49) × GCF(35, 49) = Product of 35, 49
    Prime factorization of 35 and 49 is given as, 35 = (5 × 7) = 51 × 71 and 49 = (7 × 7) = 72
    LCM(35, 49) = 245
    GCF(35, 49) = 7
    LHS = LCM(35, 49) × GCF(35, 49) = 245 × 7 = 1715
    RHS = Product of 35, 49 = 35 × 49 = 1715
    ⇒ LHS = RHS = 1715
    Hence, verified.

  3. Example 3: The GCD and LCM of two numbers are 7 and 245 respectively. If one number is 49, find the other number.

    Solution:

    Let the other number be a.
    ∵ GCD × LCM = 49 × a
    ⇒ a = (GCD × LCM)/49
    ⇒ a = (7 × 245)/49
    ⇒ a = 35
    Therefore, the other number is 35.

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FAQs on LCM of 35 and 49

What is the LCM of 35 and 49?

The LCM of 35 and 49 is 245. To find the LCM of 35 and 49, we need to find the multiples of 35 and 49 (multiples of 35 = 35, 70, 105, 140 . . . . 245; multiples of 49 = 49, 98, 147, 196 . . . . 245) and choose the smallest multiple that is exactly divisible by 35 and 49, i.e., 245.

What is the Least Perfect Square Divisible by 35 and 49?

The least number divisible by 35 and 49 = LCM(35, 49)
LCM of 35 and 49 = 5 × 7 × 7 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 35 and 49 = LCM(35, 49) × 5 = 1225 [Square root of 1225 = √1225 = ±35]
Therefore, 1225 is the required number.

If the LCM of 49 and 35 is 245, Find its GCF.

LCM(49, 35) × GCF(49, 35) = 49 × 35
Since the LCM of 49 and 35 = 245
⇒ 245 × GCF(49, 35) = 1715
Therefore, the greatest common factor = 1715/245 = 7.

Which of the following is the LCM of 35 and 49? 27, 35, 245, 30

The value of LCM of 35, 49 is the smallest common multiple of 35 and 49. The number satisfying the given condition is 245.

What are the Methods to Find LCM of 35 and 49?

The commonly used methods to find the LCM of 35 and 49 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method
 
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