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LCM of 9 and 19

LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19. The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.

1. LCM of 9 and 19
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 9 and 19?

Answer: LCM of 9 and 19 is 171.

LCM of 9 and 19

Explanation:

The LCM of two non-zero integers, x(9) and y(19), is the smallest positive integer m(171) that is divisible by both x(9) and y(19) without any remainder.

Methods to Find LCM of 9 and 19

Let's look at the different methods for finding the LCM of 9 and 19.

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

LCM of 9 and 19 by Prime Factorization

Prime factorization of 9 and 19 is (3 × 3) = 32 and (19) = 191 respectively. LCM of 9 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 32 × 191 = 171.
Hence, the LCM of 9 and 19 by prime factorization is 171.

LCM of 9 and 19 by Division Method

LCM of 9 and 19 by Division Method

To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 19. Write this prime number(3) on the left of the given numbers(9 and 19), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (9, 19) 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: Continue the steps until only 1s are left in the last row.

The LCM of 9 and 19 is the product of all prime numbers on the left, i.e. LCM(9, 19) by division method = 3 × 3 × 19 = 171.

LCM of 9 and 19 by Listing Multiples

To calculate the LCM of 9 and 19 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, . . . ) and 19 (19, 38, 57, 76, 95, . . . . )
  • Step 2: The common multiples from the multiples of 9 and 19 are 171, 342, . . .
  • Step 3: The smallest common multiple of 9 and 19 is 171.

∴ The least common multiple of 9 and 19 = 171.

☛ Also Check:

LCM of 9 and 19 Examples

  1. Example 1: The product of two numbers is 171. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 171
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 171/1
    Therefore, the LCM is 171.
    The probable combination for the given case is LCM(9, 19) = 171.

  2. Example 2: Verify the relationship between GCF and LCM of 9 and 19.

    Solution:

    The relation between GCF and LCM of 9 and 19 is given as,
    LCM(9, 19) × GCF(9, 19) = Product of 9, 19
    Prime factorization of 9 and 19 is given as, 9 = (3 × 3) = 32 and 19 = (19) = 191
    LCM(9, 19) = 171
    GCF(9, 19) = 1
    LHS = LCM(9, 19) × GCF(9, 19) = 171 × 1 = 171
    RHS = Product of 9, 19 = 9 × 19 = 171
    ⇒ LHS = RHS = 171
    Hence, verified.

  3. Example 3: The GCD and LCM of two numbers are 1 and 171 respectively. If one number is 9, find the other number.

    Solution:

    Let the other number be m.
    ∵ GCD × LCM = 9 × m
    ⇒ m = (GCD × LCM)/9
    ⇒ m = (1 × 171)/9
    ⇒ m = 19
    Therefore, the other number is 19.

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FAQs on LCM of 9 and 19

What is the LCM of 9 and 19?

The LCM of 9 and 19 is 171. To find the LCM (least common multiple) of 9 and 19, we need to find the multiples of 9 and 19 (multiples of 9 = 9, 18, 27, 36 . . . . 171; multiples of 19 = 19, 38, 57, 76 . . . . 171) and choose the smallest multiple that is exactly divisible by 9 and 19, i.e., 171.

Which of the following is the LCM of 9 and 19? 15, 30, 11, 171

The value of LCM of 9, 19 is the smallest common multiple of 9 and 19. The number satisfying the given condition is 171.

What are the Methods to Find LCM of 9 and 19?

The commonly used methods to find the LCM of 9 and 19 are:

  • Division Method
  • Listing Multiples
  • Prime Factorization Method

How to Find the LCM of 9 and 19 by Prime Factorization?

To find the LCM of 9 and 19 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (19 = 19). LCM of 9 and 19 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 19.
⇒ LCM of 9, 19 = 32 × 191 = 171.

If the LCM of 19 and 9 is 171, Find its GCF.

LCM(19, 9) × GCF(19, 9) = 19 × 9
Since the LCM of 19 and 9 = 171
⇒ 171 × GCF(19, 9) = 171
Therefore, the GCF = 171/171 = 1.

 
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