LCM of Co-prime Numbers

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.