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LCM of 2 and 7

LCM of 2 and 7 is the smallest number among all common multiples of 2 and 7. The first few multiples of 2 and 7 are (2, 4, 6, 8, 10, 12, 14, . . . ) and (7, 14, 21, 28, 35, 42, 49, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 7 - by division method, by prime factorization, and by listing multiples.

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

What is the LCM of 2 and 7?

Answer: LCM of 2 and 7 is 14.

LCM of 2 and 7

Explanation:

The LCM of two non-zero integers, x(2) and y(7), is the smallest positive integer m(14) that is divisible by both x(2) and y(7) without any remainder.

Methods to Find LCM of 2 and 7

Let's look at the different methods for finding the LCM of 2 and 7.

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

LCM of 2 and 7 by Listing Multiples

To calculate the LCM of 2 and 7 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, 14, . . . ) and 7 (7, 14, 21, 28, 35, 42, 49, . . . . )
  • Step 2: The common multiples from the multiples of 2 and 7 are 14, 28, . . .
  • Step 3: The smallest common multiple of 2 and 7 is 14.

∴ The least common multiple of 2 and 7 = 14.

LCM of 2 and 7 by Prime Factorization

Prime factorization of 2 and 7 is (2) = 21 and (7) = 71 respectively. LCM of 2 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 71 = 14.
Hence, the LCM of 2 and 7 by prime factorization is 14.

LCM of 2 and 7 by Division Method

LCM of 2 and 7 by Division Method

To calculate the LCM of 2 and 7 by the division method, we will divide the numbers(2, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 7.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 7. Write this prime number(2) on the left of the given numbers(2 and 7), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (2, 7) 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 2 and 7 is the product of all prime numbers on the left, i.e. LCM(2, 7) by division method = 2 × 7 = 14.

☛ Also Check:

LCM of 2 and 7 Examples

  1. Example 1: The product of two numbers is 14. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 14
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 14/1
    Therefore, the LCM is 14.
    The probable combination for the given case is LCM(2, 7) = 14.

  2. Example 2: The GCD and LCM of two numbers are 1 and 14 respectively. If one number is 7, find the other number.

    Solution:

    Let the other number be y.
    ∵ GCD × LCM = 7 × y
    ⇒ y = (GCD × LCM)/7
    ⇒ y = (1 × 14)/7
    ⇒ y = 2
    Therefore, the other number is 2.

  3. Example 3: Find the smallest number that is divisible by 2 and 7 exactly.

    Solution:

    The smallest number that is divisible by 2 and 7 exactly is their LCM.
    ⇒ Multiples of 2 and 7:

    • Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, . . . .
    • Multiples of 7 = 7, 14, 21, 28, 35, 42, . . . .

    Therefore, the LCM of 2 and 7 is 14.

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FAQs on LCM of 2 and 7

What is the LCM of 2 and 7?

The LCM of 2 and 7 is 14. To find the least common multiple of 2 and 7, we need to find the multiples of 2 and 7 (multiples of 2 = 2, 4, 6, 8 . . . . 14; multiples of 7 = 7, 14, 21, 28) and choose the smallest multiple that is exactly divisible by 2 and 7, i.e., 14.

How to Find the LCM of 2 and 7 by Prime Factorization?

To find the LCM of 2 and 7 using prime factorization, we will find the prime factors, (2 = 2) and (7 = 7). LCM of 2 and 7 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 7.
⇒ LCM of 2, 7 = 21 × 71 = 14.

What are the Methods to Find LCM of 2 and 7?

The commonly used methods to find the LCM of 2 and 7 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method

Which of the following is the LCM of 2 and 7? 45, 18, 14, 5

The value of LCM of 2, 7 is the smallest common multiple of 2 and 7. The number satisfying the given condition is 14.

If the LCM of 7 and 2 is 14, Find its GCF.

LCM(7, 2) × GCF(7, 2) = 7 × 2
Since the LCM of 7 and 2 = 14
⇒ 14 × GCF(7, 2) = 14
Therefore, the GCF (greatest common factor) = 14/14 = 1.

 
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