LCM (Least Common Multiple)

LCM is the smallest multiple that two or more numbers have in common. In other words, it is the smallest number that is divisible by all the given numbers.

Example:
Let's find the LCM of 4 and 6.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, ...

From the lists above, we can see that the common multiples of 4 and 6 are 12, 24, 36, ...

Therefore, the LCM of 4 and 6 is 12.

Co-Prime Numbers

Co-prime numbers, also known as relatively prime or mutually prime numbers, are numbers that have no common factors other than 1. In other words, the greatest common divisor (GCD) of co-prime numbers is always 1.

Example:
Let's consider two numbers, 8 and 9.

Factors of 8: 1, 2, 4, 8
Factors of 9: 1, 3, 9

From the lists above, we can see that the only common factor of 8 and 9 is 1.

Therefore, 8 and 9 are co-prime numbers.

Summary:
- LCM is the smallest multiple that two or more numbers have in common.
- Co-prime numbers have no common factors other than 1.

Overall, understanding LCM and co-prime numbers is important in various mathematical calculations and problem-solving.