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LCM of 1 and 5

LCM of 1 and 5 is the smallest number among all common multiples of 1 and 5. The first few multiples of 1 and 5 are (1, 2, 3, 4, 5, 6, . . . ) and (5, 10, 15, 20, 25, 30, 35, . . . ) respectively. There are 2 commonly used methods to find LCM of 1 and 5 - by division method and by listing multiples.

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

What is the LCM of 1 and 5?

Answer: LCM of 1 and 5 is 5.

LCM of 1 and 5

Explanation:

The LCM of two non-zero integers, x(1) and y(5), is the smallest positive integer m(5) that is divisible by both x(1) and y(5) without any remainder.

Methods to Find LCM of 1 and 5

Let's look at the different methods for finding the LCM of 1 and 5.

  • By Listing Multiples
  • By Division Method

LCM of 1 and 5 by Listing Multiples

To calculate the LCM of 1 and 5 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 1 (1, 2, 3, 4, 5, 6, . . . ) and 5 (5, 10, 15, 20, 25, 30, 35, . . .)
  • Step 2: The common multiples from the multiples of 1 and 5 are 5, 10, . . .
  • Step 3: The smallest common multiple of 1 and 5 is 5.

∴ The least common multiple of 1 and 5 = 5.

LCM of 1 and 5 by Division Method

LCM of 1 and 5 by Division Method

To calculate the LCM of 1 and 5 by the division method, we will divide the numbers(1, 5) by their prime factors, as long as at least one of the numbers is evenly divisible by a prime number. The product of these divisors gives the LCM of 1 and 5.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 1 and 5. Write this prime number(5) on the left of the given numbers(1 and 5), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (1, 5) 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: Since only 1s are left in the last row, we can stop the division here.

The LCM of 1 and 5 by division method is given as, LCM(1, 5) = 5.

☛ Also Check:

LCM of 1 and 5 Examples

  1. Example 1: The GCD and LCM of the two numbers are 1 and 5 respectively. If one number is 5, find the other number.

    Solution:

    Let the other number be z.
    ∵ GCD × LCM = 5 × z
    ⇒ z = (GCD × LCM)/5
    ⇒ z = (1 × 5)/5
    ⇒ z = 1
    Therefore, the other number is 1.

  2. Example 2: Find the smallest number that is divisible by 1 and 5 exactly.

    Solution:

    The smallest number that is divisible by 1 and 5 exactly is their LCM.
    ⇒ Multiples of 1 and 5:

    • Multiples of 1 = 1, 2, 3, 4, 5, 6, 7, . . . 
    • Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, . . .

    Therefore, the LCM of 1 and 5 is 5.

  3. Example 3: The product of two numbers is 5. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 5
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 5/1
    Therefore, the LCM is 5.
    The probable combination for the given case is LCM(1, 5) = 5.

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FAQs on LCM of 1 and 5

What is the LCM of 1 and 5?

The LCM of 1 and 5 is 5. To find the LCM (least common multiple) of 1 and 5, we need to find the multiples of 1 and 5 (multiples of 1 = 1, 2, 3, 4, 5, 6, . . .; multiples of 5 = 5, 10, 15, 20, . . .) and choose the smallest multiple that is exactly divisible by 1 and 5, i.e., 5.

Which of the following is the LCM of 1 and 5? 36, 18, 15, 5

The value of LCM of 1, 5 is the smallest common multiple of 1 and 5. The number satisfying the given condition is 5.

What are the Methods to Find LCM of 1 and 5?

The commonly used methods to find the LCM of 1 and 5 are:

  • Listing Multiples
  • Division Method

If the LCM of 5 and 1 is 5, Find its GCF.

LCM(5, 1) × GCF(5, 1) = 5 × 1
Since the LCM of 5 and 1 = 5
⇒ 5 × GCF(5, 1) = 5
Therefore, the GCF = 5/5 = 1.

What is the Relation Between GCF and LCM of 1, 5?

The following equation can be used to express the relation between GCF and LCM of 1 and 5, i.e. GCF × LCM = 1 × 5.

 
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