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Do two natural numbers always have a least common multiple?
Yes, two natural numbers always have a least common multiple.
Is the least common multiple of two numbers always divisible by the greatest common factor of the two numbers?
Yes, the least common multiple of two numbers is always divisible by those numbers' greatest common factor.
Is the product always the least common multiple of the numbers?
No, only if the numbers are relatively prime.
Will two numbers always have a common multiple?
A number is an exact multiple of each of a group of numbers. For example, 15 and 30 are common multiple of 3 and 5.
Is the product of two whole numbers always a common multiple of he numbers?
yes
When the greatest common factor is 1 is the least common multiple of these numbers always the product of the numbers?
Yes - if two numbers share no common factors (besides 1) the least common multiple will be the product of the numbers.
What is the greatest common multiple of 900 and 1125?
It is infinite but the lowest common multiple is 4500
Are there any pairs of prime numbers that when multiplied do not make their least common multiple?
The product of all pairs of prime numbers is always the least common multiple of the two prime numbers.
Do two whole numbers always have a least common multiple?
Yes. If A and B are any two whole numbers then A*B is a common multiple. Then either A*B is the least common multiple of A and B or one of its factors is.
Can you always find the LCM for two numbers by muiltiplying them together?
No, this will find a common multiple, but not always the least. For example, 2 and 4 have a least common multiple of 4 but if you multiply them you get 8. In fact, the LCM will only be the product of two numbers if the numbers have no common factors. We call numbers with no common factors relatively prime.
Is the least common multiple of any two numbers their product?
Sometimes, not always.
Is the least common multiple of two prime numbers always their product?
Yes.
