If two numbers are relatively prime, what is their LCM? Explain the reasoning and give 2 examples supporting the answer.
Consider the definition of relatively prime numbers:
http://wiki.answers.com/Q/What_is_a_relative_prime_number
Since they have no common prome 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.
Well, when two numbers are relatively prime, it means that they don't have any common factors other than 1. So, their least common multiple (LCM) would simply be the product of those two numbers.
Let me give you two examples to make it clearer:
Example 1:
Let's consider the numbers 4 and 9. The factors of 4 are 1, 2, and 4, while the factors of 9 are 1, 3, and 9. As you can see, the only factor that 4 and 9 have in common is 1. So, their LCM would just be the product of the two numbers, which is 4 * 9 = 36.
Example 2:
Now, let's take the numbers 7 and 10. The factors of 7 are only 1 and 7, while the factors of 10 are 1, 2, 5, and 10. Again, the only factor that these two numbers have in common is 1, so their LCM would be the product of 7 and 10, which is 7 * 10 = 70.
So, in both cases, the LCM of two relatively prime numbers is simply the product of those two numbers.
If two numbers are relatively prime, their least common multiple (LCM) is equal to the product of the two numbers.
The reasoning behind this is that when two numbers are relatively prime, it means they have no common factors other than 1. This implies that their LCM does not have any factors other than the numbers themselves and 1.
To find the LCM of two relatively prime numbers, we multiply them together. This is because the LCM needs to be divisible by both numbers, and when two numbers are relatively prime, their only common factor is 1. Therefore, their product is the smallest number that is divisible by both of them.
Example 1:
Let's take two relatively prime numbers: 7 and 11.
7 and 11 have no common factors other than 1.
The product of 7 and 11 is 77.
Therefore, the LCM of 7 and 11 is 77.
Example 2:
Consider two relatively prime numbers: 5 and 13.
5 and 13 have no common factors other than 1.
The product of 5 and 13 is 65.
Hence, the LCM of 5 and 13 is 65.
In both examples, the LCM is equal to the product of the two numbers, confirming the statement that when two numbers are relatively prime, their LCM is equal to their product.
When two numbers are relatively prime, it means that they have no common factors other than 1. The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers without leaving a remainder.
To find the LCM of two relatively prime numbers, you multiply the two numbers together because there are no common factors to consider. Since there are no common factors, the resulting product will be the LCM.
Let's take two relatively prime numbers, 6 and 7, as an example. The factors of 6 are 1, 2, 3, and 6, while the factors of 7 are only 1 and 7. The LCM of 6 and 7 is simply their product, which is 6 x 7 = 42.
Another example could be the numbers 15 and 17, which are also relatively prime. The factors of 15 are 1, 3, 5, and 15, while the factors of 17 are only 1 and 17. Therefore, the LCM of 15 and 17 is 15 x 17 = 255.
To recap, when two numbers are relatively prime, their LCM is equal to their product because there are no common factors between them. Examples such as 6 and 7 or 15 and 17 demonstrate this principle.