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LCM of 5 and 16

LCM of 5 and 16 is the smallest number among all common multiples of 5 and 16. The first few multiples of 5 and 16 are (5, 10, 15, 20, 25, . . . ) and (16, 32, 48, 64, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 16 - by listing multiples, by prime factorization, and by division method.

1. LCM of 5 and 16
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 5 and 16?

Answer: LCM of 5 and 16 is 80.

LCM of 5 and 16

Explanation:

The LCM of two non-zero integers, x(5) and y(16), is the smallest positive integer m(80) that is divisible by both x(5) and y(16) without any remainder.

Methods to Find LCM of 5 and 16

Let's look at the different methods for finding the LCM of 5 and 16.

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

LCM of 5 and 16 by Listing Multiples

To calculate the LCM of 5 and 16 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, . . . ) and 16 (16, 32, 48, 64, . . . . )
  • Step 2: The common multiples from the multiples of 5 and 16 are 80, 160, . . .
  • Step 3: The smallest common multiple of 5 and 16 is 80.

∴ The least common multiple of 5 and 16 = 80.

LCM of 5 and 16 by Prime Factorization

Prime factorization of 5 and 16 is (5) = 51 and (2 × 2 × 2 × 2) = 24 respectively. LCM of 5 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 51 = 80.
Hence, the LCM of 5 and 16 by prime factorization is 80.

LCM of 5 and 16 by Division Method

LCM of 5 and 16 by Division Method

To calculate the LCM of 5 and 16 by the division method, we will divide the numbers(5, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 16.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 16. Write this prime number(2) on the left of the given numbers(5 and 16), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (5, 16) 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 5 and 16 is the product of all prime numbers on the left, i.e. LCM(5, 16) by division method = 2 × 2 × 2 × 2 × 5 = 80.

☛ Also Check:

LCM of 5 and 16 Examples

  1. Example 1: The GCD and LCM of two numbers are 1 and 80 respectively. If one number is 16, find the other number.

    Solution:

    Let the other number be z.
    ∵ GCD × LCM = 16 × z
    ⇒ z = (GCD × LCM)/16
    ⇒ z = (1 × 80)/16
    ⇒ z = 5
    Therefore, the other number is 5.

  2. Example 2: Verify the relationship between GCF and LCM of 5 and 16.

    Solution:

    The relation between GCF and LCM of 5 and 16 is given as,
    LCM(5, 16) × GCF(5, 16) = Product of 5, 16
    Prime factorization of 5 and 16 is given as, 5 = (5) = 51 and 16 = (2 × 2 × 2 × 2) = 24
    LCM(5, 16) = 80
    GCF(5, 16) = 1
    LHS = LCM(5, 16) × GCF(5, 16) = 80 × 1 = 80
    RHS = Product of 5, 16 = 5 × 16 = 80
    ⇒ LHS = RHS = 80
    Hence, verified.

  3. Example 3: The product of two numbers is 80. If their GCD is 1, what is their LCM?

    Solution:

    Given: GCD = 1
    product of numbers = 80
    ∵ LCM × GCD = product of numbers
    ⇒ LCM = Product/GCD = 80/1
    Therefore, the LCM is 80.
    The probable combination for the given case is LCM(5, 16) = 80.

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FAQs on LCM of 5 and 16

What is the LCM of 5 and 16?

The LCM of 5 and 16 is 80. To find the least common multiple of 5 and 16, we need to find the multiples of 5 and 16 (multiples of 5 = 5, 10, 15, 20 . . . . 80; multiples of 16 = 16, 32, 48, 64 . . . . 80) and choose the smallest multiple that is exactly divisible by 5 and 16, i.e., 80.

What is the Relation Between GCF and LCM of 5, 16?

The following equation can be used to express the relation between GCF and LCM of 5 and 16, i.e. GCF × LCM = 5 × 16.

How to Find the LCM of 5 and 16 by Prime Factorization?

To find the LCM of 5 and 16 using prime factorization, we will find the prime factors, (5 = 5) and (16 = 2 × 2 × 2 × 2). LCM of 5 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 5 and 16.
⇒ LCM of 5, 16 = 24 × 51 = 80.

If the LCM of 16 and 5 is 80, Find its GCF.

LCM(16, 5) × GCF(16, 5) = 16 × 5
Since the LCM of 16 and 5 = 80
⇒ 80 × GCF(16, 5) = 80
Therefore, the GCF (greatest common factor) = 80/80 = 1.

What are the Methods to Find LCM of 5 and 16?

The commonly used methods to find the LCM of 5 and 16 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples
 
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