Yes, as long as the numbers are positive.
True.
No, only if the numbers are relatively prime.
The LCM or least common multiple is 253. In this case, the greatest common factor of the two numbers is 1. That is to say, they have no other common factors. We call these numbers relatively prime. When two numbers are relatively prime their LCM is always the product of the two numbers.Sometimes it is easier to find the greatest common factor than to find the least common multiple by looking at multiples of both numbers. This is true if the numbers are primes like 11 and 23. So if you are give two primes, the LCM will always be the product of the two numbers.
The answer is sometimes - when the multiple in question is 1.
There is really no such thing as a "greatest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.
The LCM of prime numbers is simply their product (a x b, or x*y). The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of two prime numbers is 1. Therefore, the least common multiple of two prime numbers is the two numbers multiplied together, since dividing by 1 will not change the answer. The same applies to "relatively prime" numbers such as 10 and 21, where the GCF is also 1.
Yes - if two numbers share no common factors (besides 1) the least common multiple will be the product of the numbers.
Yes, the least common multiple of two numbers is always divisible by those numbers' greatest common factor.
No, only if the numbers are relatively prime.
yes
7 times 23. The product of 2 numbers is always a common multiple but not necessarily the least. Question for you : When is the LCM the product ? Think about the relation between the product, the LCM and the Greatest Common Factor.
The LCM or least common multiple is 253. In this case, the greatest common factor of the two numbers is 1. That is to say, they have no other common factors. We call these numbers relatively prime. When two numbers are relatively prime their LCM is always the product of the two numbers.Sometimes it is easier to find the greatest common factor than to find the least common multiple by looking at multiples of both numbers. This is true if the numbers are primes like 11 and 23. So if you are give two primes, the LCM will always be the product of the two numbers.
The answer is sometimes - when the multiple in question is 1.
Sometimes, not always.
Yes.
There is really no such thing as a "greatest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.
Trees aren't necessary. The greatest common multiple of any set of numbers is always infinite.
Greatest common multiple of two prime numbers is always 1. Therefore, gcf of 11 and 17 is 1.