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LCM of 46 and 51

LCM of 46 and 51 is the smallest number among all common multiples of 46 and 51. The first few multiples of 46 and 51 are (46, 92, 138, 184, 230, 276, . . . ) and (51, 102, 153, 204, 255, 306, . . . ) respectively. There are 3 commonly used methods to find LCM of 46 and 51 - by division method, by listing multiples, and by prime factorization.

1. LCM of 46 and 51
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 46 and 51?

Answer: LCM of 46 and 51 is 2346.

LCM of 46 and 51

Explanation:

The LCM of two non-zero integers, x(46) and y(51), is the smallest positive integer m(2346) that is divisible by both x(46) and y(51) without any remainder.

Methods to Find LCM of 46 and 51

The methods to find the LCM of 46 and 51 are explained below.

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

LCM of 46 and 51 by Prime Factorization

Prime factorization of 46 and 51 is (2 × 23) = 21 × 231 and (3 × 17) = 31 × 171 respectively. LCM of 46 and 51 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 171 × 231 = 2346.
Hence, the LCM of 46 and 51 by prime factorization is 2346.

LCM of 46 and 51 by Division Method

LCM of 46 and 51 by Division Method

To calculate the LCM of 46 and 51 by the division method, we will divide the numbers(46, 51) by their prime factors (preferably common). The product of these divisors gives the LCM of 46 and 51.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 46 and 51. Write this prime number(2) on the left of the given numbers(46 and 51), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (46, 51) 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 46 and 51 is the product of all prime numbers on the left, i.e. LCM(46, 51) by division method = 2 × 3 × 17 × 23 = 2346.

LCM of 46 and 51 by Listing Multiples

To calculate the LCM of 46 and 51 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 46 (46, 92, 138, 184, 230, 276, . . . ) and 51 (51, 102, 153, 204, 255, 306, . . . . )
  • Step 2: The common multiples from the multiples of 46 and 51 are 2346, 4692, . . .
  • Step 3: The smallest common multiple of 46 and 51 is 2346.

∴ The least common multiple of 46 and 51 = 2346.

☛ Also Check:

LCM of 46 and 51 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 46 and 51.

    Solution:

    The relation between GCF and LCM of 46 and 51 is given as,
    LCM(46, 51) × GCF(46, 51) = Product of 46, 51
    Prime factorization of 46 and 51 is given as, 46 = (2 × 23) = 21 × 231 and 51 = (3 × 17) = 31 × 171
    LCM(46, 51) = 2346
    GCF(46, 51) = 1
    LHS = LCM(46, 51) × GCF(46, 51) = 2346 × 1 = 2346
    RHS = Product of 46, 51 = 46 × 51 = 2346
    ⇒ LHS = RHS = 2346
    Hence, verified.

  2. Example 2: The product of two numbers is 2346. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 2346
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 2346/1
    Therefore, the LCM is 2346.
    The probable combination for the given case is LCM(46, 51) = 2346.

  3. Example 3: The GCD and LCM of two numbers are 1 and 2346 respectively. If one number is 51, find the other number.

    Solution:

    Let the other number be b.
    ∵ GCD × LCM = 51 × b
    ⇒ b = (GCD × LCM)/51
    ⇒ b = (1 × 2346)/51
    ⇒ b = 46
    Therefore, the other number is 46.

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FAQs on LCM of 46 and 51

What is the LCM of 46 and 51?

The LCM of 46 and 51 is 2346. To find the least common multiple (LCM) of 46 and 51, we need to find the multiples of 46 and 51 (multiples of 46 = 46, 92, 138, 184 . . . . 2346; multiples of 51 = 51, 102, 153, 204 . . . . 2346) and choose the smallest multiple that is exactly divisible by 46 and 51, i.e., 2346.

What is the Relation Between GCF and LCM of 46, 51?

The following equation can be used to express the relation between GCF and LCM of 46 and 51, i.e. GCF × LCM = 46 × 51.

What are the Methods to Find LCM of 46 and 51?

The commonly used methods to find the LCM of 46 and 51 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples

If the LCM of 51 and 46 is 2346, Find its GCF.

LCM(51, 46) × GCF(51, 46) = 51 × 46
Since the LCM of 51 and 46 = 2346
⇒ 2346 × GCF(51, 46) = 2346
Therefore, the GCF = 2346/2346 = 1.

Which of the following is the LCM of 46 and 51? 15, 24, 28, 2346

The value of LCM of 46, 51 is the smallest common multiple of 46 and 51. The number satisfying the given condition is 2346.

 
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