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LCM of 10 and 40

LCM of 10 and 40 is the smallest number among all common multiples of 10 and 40. The first few multiples of 10 and 40 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (40, 80, 120, 160, 200, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 40 - by division method, by prime factorization, and by listing multiples.

1. LCM of 10 and 40
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 10 and 40?

Answer: LCM of 10 and 40 is 40.

LCM of 10 and 40

Explanation:

The LCM of two non-zero integers, x(10) and y(40), is the smallest positive integer m(40) that is divisible by both x(10) and y(40) without any remainder.

Methods to Find LCM of 10 and 40

The methods to find the LCM of 10 and 40 are explained below.

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

LCM of 10 and 40 by Prime Factorization

Prime factorization of 10 and 40 is (2 × 5) = 21 × 51 and (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM of 10 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 51 = 40.
Hence, the LCM of 10 and 40 by prime factorization is 40.

LCM of 10 and 40 by Listing Multiples

To calculate the LCM of 10 and 40 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, 70, . . . ) and 40 (40, 80, 120, 160, 200, 240, . . . . )
  • Step 2: The common multiples from the multiples of 10 and 40 are 40, 80, . . .
  • Step 3: The smallest common multiple of 10 and 40 is 40.

∴ The least common multiple of 10 and 40 = 40.

LCM of 10 and 40 by Division Method

LCM of 10 and 40 by Division Method

To calculate the LCM of 10 and 40 by the division method, we will divide the numbers(10, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 40.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 40. Write this prime number(2) on the left of the given numbers(10 and 40), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (10, 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 10 and 40 is the product of all prime numbers on the left, i.e. LCM(10, 40) by division method = 2 × 2 × 2 × 5 = 40.

☛ Also Check:

LCM of 10 and 40 Examples

  1. Example 1: The product of two numbers is 400. If their GCD is 10, what is their LCM?

    Solution:

    Given: GCD = 10
    product of numbers = 400
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 400/10
    Therefore, the LCM is 40.
    The probable combination for the given case is LCM(10, 40) = 40.

  2. Example 2: Find the smallest number that is divisible by 10 and 40 exactly.

    Solution:

    The smallest number that is divisible by 10 and 40 exactly is their LCM.
    ⇒ Multiples of 10 and 40:

    • Multiples of 10 = 10, 20, 30, 40, 50, 60, . . . .
    • Multiples of 40 = 40, 80, 120, 160, 200, 240, . . . .

    Therefore, the LCM of 10 and 40 is 40.

  3. Example 3: Verify the relationship between GCF and LCM of 10 and 40.

    Solution:

    The relation between GCF and LCM of 10 and 40 is given as,
    LCM(10, 40) × GCF(10, 40) = Product of 10, 40
    Prime factorization of 10 and 40 is given as, 10 = (2 × 5) = 21 × 51 and 40 = (2 × 2 × 2 × 5) = 23 × 51
    LCM(10, 40) = 40
    GCF(10, 40) = 10
    LHS = LCM(10, 40) × GCF(10, 40) = 40 × 10 = 400
    RHS = Product of 10, 40 = 10 × 40 = 400
    ⇒ LHS = RHS = 400
    Hence, verified.

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FAQs on LCM of 10 and 40

What is the LCM of 10 and 40?

The LCM of 10 and 40 is 40. To find the LCM (least common multiple) of 10 and 40, we need to find the multiples of 10 and 40 (multiples of 10 = 10, 20, 30, 40; multiples of 40 = 40, 80, 120, 160) and choose the smallest multiple that is exactly divisible by 10 and 40, i.e., 40.

What are the Methods to Find LCM of 10 and 40?

The commonly used methods to find the LCM of 10 and 40 are:

  • Listing Multiples
  • Division Method
  • Prime Factorization Method

What is the Relation Between GCF and LCM of 10, 40?

The following equation can be used to express the relation between GCF and LCM of 10 and 40, i.e. GCF × LCM = 10 × 40.

Which of the following is the LCM of 10 and 40? 40, 28, 5, 45

The value of LCM of 10, 40 is the smallest common multiple of 10 and 40. The number satisfying the given condition is 40.

If the LCM of 40 and 10 is 40, Find its GCF.

LCM(40, 10) × GCF(40, 10) = 40 × 10
Since the LCM of 40 and 10 = 40
⇒ 40 × GCF(40, 10) = 400
Therefore, the GCF = 400/40 = 10.

 
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