LCM of Co-prime Numbers
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Questions and Answers

If two numbers are co-prime, their GCD is always greater than 1.

False

The LCM of two co-prime numbers is equal to their sum.

False

Co-prime numbers always have a common factor other than 1.

False

The LCM of two co-prime numbers can be calculated using their GCD.

<p>False</p> Signup and view all the answers

The LCM of two co-prime numbers is always equal to their product.

<p>True</p> Signup and view all the answers

Study Notes

LCM of Co-prime Numbers

Definition: Two numbers are said to be co-prime (or mutually prime) if their greatest common divisor (GCD) is 1.

Properties:

  • The LCM of two co-prime numbers is equal to the product of the two numbers.
  • If a and b are co-prime, then LCM(a, b) = a × b
  • This is because the only common factor of two co-prime numbers is 1, so the LCM is the product of the two numbers.

Example: Find the LCM of 8 and 15.

  • Since 8 and 15 are co-prime (GCD(8, 15) = 1), the LCM is equal to their product: LCM(8, 15) = 8 × 15 = 120

Key Points:

  • The LCM of two co-prime numbers is always equal to their product.
  • Co-prime numbers do not have any common factors other than 1.
  • This property can be used to simplify calculations involving LCM of co-prime numbers.

Co-prime Numbers and LCM

  • Co-prime numbers are two numbers with a greatest common divisor (GCD) of 1.
  • The LCM of two co-prime numbers is equal to the product of the two numbers.

Properties of Co-prime Numbers and LCM

  • If a and b are co-prime, then LCM(a, b) = a × b.
  • The only common factor of two co-prime numbers is 1, making the LCM the product of the two numbers.

Example of LCM of Co-prime Numbers

  • LCM of 8 and 15 is 120, as 8 and 15 are co-prime (GCD(8, 15) = 1).

Key Points to Remember

  • The LCM of two co-prime numbers is always equal to their product.
  • Co-prime numbers do not have any common factors other than 1.
  • This property can be used to simplify calculations involving LCM of co-prime numbers.

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Description

This quiz covers the properties and examples of finding the least common multiple (LCM) of co-prime numbers, including the formula and its application.

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