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LCM of 5 and 40

LCM of 5 and 40 is the smallest number among all common multiples of 5 and 40. The first few multiples of 5 and 40 are (5, 10, 15, 20, 25, 30, . . . ) and (40, 80, 120, 160, 200, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 40 - by division method, by prime factorization, and by listing multiples.

1. LCM of 5 and 40
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 5 and 40?

Answer: LCM of 5 and 40 is 40.

LCM of 5 and 40

Explanation:

The LCM of two non-zero integers, x(5) and y(40), is the smallest positive integer m(40) that is divisible by both x(5) and y(40) without any remainder.

Methods to Find LCM of 5 and 40

Let's look at the different methods for finding the LCM of 5 and 40.

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

LCM of 5 and 40 by Division Method

LCM of 5 and 40 by Division Method

To calculate the LCM of 5 and 40 by the division method, we will divide the numbers(5, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 40.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 40. Write this prime number(2) on the left of the given numbers(5 and 40), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (5, 40) 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 5 and 40 is the product of all prime numbers on the left, i.e. LCM(5, 40) by division method = 2 × 2 × 2 × 5 = 40.

LCM of 5 and 40 by Prime Factorization

Prime factorization of 5 and 40 is (5) = 51 and (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM of 5 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 51 = 40.
Hence, the LCM of 5 and 40 by prime factorization is 40.

LCM of 5 and 40 by Listing Multiples

To calculate the LCM of 5 and 40 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 40 (40, 80, 120, 160, 200, 240, . . . . )
  • Step 2: The common multiples from the multiples of 5 and 40 are 40, 80, . . .
  • Step 3: The smallest common multiple of 5 and 40 is 40.

∴ The least common multiple of 5 and 40 = 40.

☛ Also Check:

LCM of 5 and 40 Examples

  1. Example 1: Verify the relationship between GCF and LCM of 5 and 40.

    Solution:

    The relation between GCF and LCM of 5 and 40 is given as,
    LCM(5, 40) × GCF(5, 40) = Product of 5, 40
    Prime factorization of 5 and 40 is given as, 5 = (5) = 51 and 40 = (2 × 2 × 2 × 5) = 23 × 51
    LCM(5, 40) = 40
    GCF(5, 40) = 5
    LHS = LCM(5, 40) × GCF(5, 40) = 40 × 5 = 200
    RHS = Product of 5, 40 = 5 × 40 = 200
    ⇒ LHS = RHS = 200
    Hence, verified.

  2. Example 2: The product of two numbers is 200. If their GCD is 5, what is their LCM?

    Solution:

    Given: GCD = 5
    product of numbers = 200
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 200/5
    Therefore, the LCM is 40.
    The probable combination for the given case is LCM(5, 40) = 40.

  3. Example 3: The GCD and LCM of two numbers are 5 and 40 respectively. If one number is 5, find the other number.

    Solution:

    Let the other number be b.
    ∵ GCD × LCM = 5 × b
    ⇒ b = (GCD × LCM)/5
    ⇒ b = (5 × 40)/5
    ⇒ b = 40
    Therefore, the other number is 40.

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FAQs on LCM of 5 and 40

What is the LCM of 5 and 40?

The LCM of 5 and 40 is 40. To find the LCM (least common multiple) of 5 and 40, we need to find the multiples of 5 and 40 (multiples of 5 = 5, 10, 15, 20 . . . . 40; multiples of 40 = 40, 80, 120, 160) and choose the smallest multiple that is exactly divisible by 5 and 40, i.e., 40.

What is the Least Perfect Square Divisible by 5 and 40?

The least number divisible by 5 and 40 = LCM(5, 40)
LCM of 5 and 40 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 5 and 40 = LCM(5, 40) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

If the LCM of 40 and 5 is 40, Find its GCF.

LCM(40, 5) × GCF(40, 5) = 40 × 5
Since the LCM of 40 and 5 = 40
⇒ 40 × GCF(40, 5) = 200
Therefore, the GCF = 200/40 = 5.

What are the Methods to Find LCM of 5 and 40?

The commonly used methods to find the LCM of 5 and 40 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method

Which of the following is the LCM of 5 and 40? 32, 5, 40, 3

The value of LCM of 5, 40 is the smallest common multiple of 5 and 40. The number satisfying the given condition is 40.

 
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