Drwls - totally confused me on how this problem is done. Can someone else help to solve this problem?
If two numbers are relatively prime, what is their LCM? Explain the reasoning and give 2 examples supporting the answer.
Did you carefully read all the information in the web site he posted?
If a number is prime then you know that it's a multiple of itself and the number 1.
Example: Multiples for 7 are 7 & 1
Example: Multiples for 23 are 23 and 1
If you wanted to find the the LCM of both it would have to be 23 x 7
Do you understand why? There is no number other than 1 that can divide into both.
If you had non-prime numbers like 4 and 2, their LCM would be 4 since 2x2=4 and 1x4=4.
I don't know if I'm doing a good job explaining this or if I'm confusing you more but I tried.
The multiples of 7 are not 7 and 1, rather what I meant to say is that 1x7 =7, the multiples of 7 would be 7,14,21 ect. Sorry if that confused you. Same with the number 23.
The factors for 7 are 1 and 7
The factors for 23 are 1 and 23
"Since they have no common prime factors between them other than one, the Least Common Multiple must contain all the prime factors of both, making it the product of the two numbers."
This is what drwls posted, and to me it is crystal clear... unless you did not read what he wrote, just scanning for numbers.
I'd be happy to help you understand the concept of finding the LCM (Least Common Multiple) of two relatively prime numbers!
To start, two numbers are considered relatively prime if they have no common prime factors. In other words, they do not share any prime factors other than 1. For example, 8 and 9 are relatively prime since 8 = 2^3 (no common factors) and 9 = 3^2 (no common factors as well).
When two numbers are relatively prime, their LCM is simply the product of the two numbers. This is because, without any common factors, the LCM can be found by multiplying the two numbers together.
Let's take two examples to illustrate this:
Example 1: Let's find the LCM of 6 and 7.
Since 6 and 7 are relatively prime, we can directly multiply them: LCM(6, 7) = 6 * 7 = 42
Example 2: Let's find the LCM of 10 and 13.
Again, since 10 and 13 are relatively prime, we multiply them together: LCM(10, 13) = 10 * 13 = 130
In both cases, the LCM of two relatively prime numbers is simply the product of those numbers. This is because there are no common factors that need to be considered when finding the LCM.
I hope this explanation clarifies the concept for you! Let me know if you have any further questions.