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LCM of 3 and 1

LCM of 3 and 1 is the smallest number among all common multiples of 3 and 1. The first few multiples of 3 and 1 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (1, 2, 3, 4, 5, . . . ) respectively. There are 2 commonly used methods to find LCM of 3 and 1 - by division method, and by listing multiples.

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

What is the LCM of 3 and 1?

Answer: LCM of 3 and 1 is 3.

LCM of 3 and 1

Explanation:

The LCM of two non-zero integers, x(3) and y(1), is the smallest positive integer m(3) that is divisible by both x(3) and y(1) without any remainder.

Methods to Find LCM of 3 and 1

Let's look at the different methods for finding the LCM of 3 and 1.

  • By Division Method
  • By Listing Multiples

LCM of 3 and 1 by Division Method

To calculate the LCM of 3 and 1 by the division method, we will divide the numbers(3, 1) 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 3 and 1.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 1. Write this prime number(3) on the left of the given numbers(3 and 1), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (3, 1) is a multiple of 3, divide it by 3 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 here.

The LCM of 3 and 1 by division method is given as, LCM(3, 1) = 3.

LCM of 3 and 1 by Listing Multiples

LCM of 3 and 1 by Listing Multiples Method

To calculate the LCM of 3 and 1 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 1 (1, 2, 3, 4, 5, . . . )
  • Step 2: The common multiples from the multiples of 3 and 1 are 3, 6, . . .
  • Step 3: The smallest common multiple of 3 and 1 is 3.

∴ The least common multiple of 3 and 1 = 3.

☛ Also Check:

LCM of 3 and 1 Examples

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

    Solution:

    Let the other number be z.
    ∵ GCD × LCM = 3 × z
    ⇒ z = (GCD × LCM)/3
    ⇒ z = (1 × 3)/3
    ⇒ z = 1
    Therefore, the other number is 1.

  2. Example 2: The product of two numbers is 3. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 3
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 3/1
    Therefore, the LCM is 3.
    The probable combination for the given case is LCM(3, 1) = 3.

  3. Example 3: Find the smallest number that is divisible by 3 and 1 exactly.

    Solution:

    The smallest number that is divisible by 3 and 1 exactly is their LCM.
    ⇒ Multiples of 3 and 1:

    • Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, . . .
    • Multiples of 1 = 1, 2, 3, 4, 5, 6, 7, . . .

    Therefore, the LCM of 3 and 1 is 3.

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FAQs on LCM of 3 and 1

What is the LCM of 3 and 1?

The LCM of 3 and 1 is 3. To find the least common multiple (LCM) of 3 and 1, we need to find the multiples of 3 and 1 (multiples of 3 = 3, 6, 9, 12, . . .; multiples of 1 = 1, 2, 3, 4, . . .) and choose the smallest multiple that is exactly divisible by 3 and 1, i.e., 3.

What is the Relation Between GCF and LCM of 3, 1?

The following equation can be used to express the relation between GCF and LCM of 3 and 1, i.e. GCF × LCM = 3 × 1.

If the LCM of 1 and 3 is 3, Find its GCF.

LCM(1, 3) × GCF(1, 3) = 1 × 3
Since the LCM of 1 and 3 = 3
⇒ 3 × GCF(1, 3) = 3
Therefore, the GCF = 3/3 = 1.

What is the Least Perfect Square Divisible by 3 and 1?

The least number divisible by 3 and 1 = LCM(3, 1)
LCM of 3 and 1 = 3
⇒ Least perfect square divisible by each 3 and 1 = 3 × 3 = 9 [Square root of 9 = √9 = ±3]
Therefore, 9 is the required number.

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
 
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