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Q: When the greatest common factor is 1 is the least common multiple of these numbers always the product of the numbers?

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No, not always.

Yes, as long as the numbers are positive.

Yes.

yes

Yes, the least common multiple of two numbers is always divisible by those numbers' greatest common factor.

Sometimes, not always.

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.

There is no greatest common multiple of two numbers. For whatever number you come up with I can always add the lowest common multiple of the numbers to get an even higher common multiple.

Sometimes, not always.

Yes.

The answer is sometimes - when the multiple in question is 1.

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.

No, only if the numbers are relatively prime.

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.

Not always. The product of two numbers will always be a common multiple, but it will not always be least. The product of 4 and 9 is 36. The LCM of 4 and 9 is 36. The product of 4 and 8 is 32. The LCM of 4 and 8 is 16.

The product of all pairs of prime numbers is always the least common multiple of the two prime numbers.

Multiplying two numbers together will create a common multiple. It is sometimes, but not always, the LCM as well.

The greatest common multiple of any set of integers is infinite.

Why the product of a multiple of ten and a multiple of ten will always have only one zero

It's always a common multiple; it's not always least. Simple counter example: 4 × 6 = 24 But LCM(4, 6) = 12 ------------------------------------------------------------------------------------ Note: HCF(4, 6) = 2 What is true of any two whole numbers that the product of the two numbers is equal to the product of their highest common factor and lowest common multiple. eg 4 × 6 = hcf(4, 6) × lcm(4, 6) = 2 × 12 = 24.

Because each of the numbers is a multiple of 3, so their product will be a multiple of 3 x 3 = 9. Algebraically: let the two numbers from the 3 times table be 3m and 3n for some m and n. Their product is 3m x 3n = (3 x 3)mn = 9mn, a multiple of 9.

There is no greatest multiple of any number: whatever multiple of 4 you say is the greatest I can always add 4 and get an even greater multiple.

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.

No, 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.