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LCM of 3 and 30

LCM of 3 and 30 is the smallest number among all common multiples of 3 and 30. The first few multiples of 3 and 30 are (3, 6, 9, 12, . . . ) and (30, 60, 90, 120, 150, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 30 - by listing multiples, by division method, and by prime factorization.

1. LCM of 3 and 30
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 3 and 30?

Answer: LCM of 3 and 30 is 30.

LCM of 3 and 30

Explanation:

The LCM of two non-zero integers, x(3) and y(30), is the smallest positive integer m(30) that is divisible by both x(3) and y(30) without any remainder.

Methods to Find LCM of 3 and 30

Let's look at the different methods for finding the LCM of 3 and 30.

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

LCM of 3 and 30 by Prime Factorization

Prime factorization of 3 and 30 is (3) = 31 and (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM of 3 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 = 30.
Hence, the LCM of 3 and 30 by prime factorization is 30.

LCM of 3 and 30 by Listing Multiples

To calculate the LCM of 3 and 30 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, . . . ) and 30 (30, 60, 90, 120, 150, 180, . . . . )
  • Step 2: The common multiples from the multiples of 3 and 30 are 30, 60, . . .
  • Step 3: The smallest common multiple of 3 and 30 is 30.

∴ The least common multiple of 3 and 30 = 30.

LCM of 3 and 30 by Division Method

LCM of 3 and 30 by Division Method

To calculate the LCM of 3 and 30 by the division method, we will divide the numbers(3, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 30.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 30. Write this prime number(2) on the left of the given numbers(3 and 30), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (3, 30) 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 3 and 30 is the product of all prime numbers on the left, i.e. LCM(3, 30) by division method = 2 × 3 × 5 = 30.

☛ Also Check:

LCM of 3 and 30 Examples

  1. Example 1: The product of two numbers is 90. If their GCD is 3, what is their LCM?

    Solution:

    Given: GCD = 3
    product of numbers = 90
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 90/3
    Therefore, the LCM is 30.
    The probable combination for the given case is LCM(3, 30) = 30.

  2. Example 2: The GCD and LCM of two numbers are 3 and 30 respectively. If one number is 3, find the other number.

    Solution:

    Let the other number be m.
    ∵ GCD × LCM = 3 × m
    ⇒ m = (GCD × LCM)/3
    ⇒ m = (3 × 30)/3
    ⇒ m = 30
    Therefore, the other number is 30.

  3. Example 3: Verify the relationship between GCF and LCM of 3 and 30.

    Solution:

    The relation between GCF and LCM of 3 and 30 is given as,
    LCM(3, 30) × GCF(3, 30) = Product of 3, 30
    Prime factorization of 3 and 30 is given as, 3 = (3) = 31 and 30 = (2 × 3 × 5) = 21 × 31 × 51
    LCM(3, 30) = 30
    GCF(3, 30) = 3
    LHS = LCM(3, 30) × GCF(3, 30) = 30 × 3 = 90
    RHS = Product of 3, 30 = 3 × 30 = 90
    ⇒ LHS = RHS = 90
    Hence, verified.

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FAQs on LCM of 3 and 30

What is the LCM of 3 and 30?

The LCM of 3 and 30 is 30. To find the least common multiple (LCM) of 3 and 30, we need to find the multiples of 3 and 30 (multiples of 3 = 3, 6, 9, 12 . . . . 30; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 3 and 30, i.e., 30.

What are the Methods to Find LCM of 3 and 30?

The commonly used methods to find the LCM of 3 and 30 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method

If the LCM of 30 and 3 is 30, Find its GCF.

LCM(30, 3) × GCF(30, 3) = 30 × 3
Since the LCM of 30 and 3 = 30
⇒ 30 × GCF(30, 3) = 90
Therefore, the greatest common factor = 90/30 = 3.

How to Find the LCM of 3 and 30 by Prime Factorization?

To find the LCM of 3 and 30 using prime factorization, we will find the prime factors, (3 = 3) and (30 = 2 × 3 × 5). LCM of 3 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 30.
⇒ LCM of 3, 30 = 21 × 31 × 51 = 30.

What is the Relation Between GCF and LCM of 3, 30?

The following equation can be used to express the relation between GCF and LCM of 3 and 30, i.e. GCF × LCM = 3 × 30.

 
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