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Why is the product of greatest common factor and least common multiple the same as the product of the original pair of numbers?
The prime factorization of 24 is 2 x 2 x 2 x 3
The prime factorization of 36 is 2 x 2 x 3 x 3
Their product, 864, is the combination of those factors: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
The prime factorization of their GCF, 12, is 2 x 2 x 3
The prime factorization of their LCM, 72, is 2 x 2 x 2 x 3 x 3
Their product, 864, is the combination of those factors: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
It's the same pool of factors.
What else can I help you with?
What is the least common multiple of 5 and 23?
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 5 and 23 is 1. (See related question "What is the greatest common factor of 5 and 23?" for this calculation.) So, the least common multiple is 5 x 23 ÷ 1 = 115.
Is the product of two counting numbers a multiple of those numbers?
Yes. It's a multiple of each of them.
Is a factor the product of any two whole numbers?
No, the factors are the whole numbers. The product is the multiple.
Do multiples and product mean the same?
No, multiples and product do not mean the same thing. Multiples are the result of multiplying a number by an integer, resulting in a sequence of numbers that are all divisible by the original number. The product, on the other hand, is the result of multiplying two or more numbers together. In simpler terms, multiples are the numbers in the times table of a given number, while the product is the result of multiplying numbers.
What is The product of that number and any nonzero whole number?
This product is called a multiple of the original number.
Can you predict what the least common multiple will be if the greatest common factor of two numbers is 1?
Yes, the LCM will be the product of the original two numbers.
When is the product of two numbers divided by the greatest common multiple the least common multiple?
Never. The greatest common multiple of any two numbers is infinite.
How do you find the least common multiple using the greatest common factor?
Multiply the original two numbers. Divide that product by their GCF. The result is their LCM.
What is the greatest common multiple of two prime numbers?
The greatest common multiple is an infinite amount and not very practical for problem solving. The least common multiple of two prime numbers is their product.
What is it when prime numbers are multiplied together to get the original number?
Then, we obtain the multiple or the product of prime numbers.
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.
Can you predict the least common multiple of two numbers if the greatest common factor is one?
No, you need at least two numbers to compare in order to find a greatest common factor.
What is the relationship does the greatest common factor and the LCM have?
The product of the GCF and LCM is equal to the product of the original two numbers.
If the greatest common factor of two whole numbers is 1 what is the least common multiple of the numbers?
The LCM of the two numbers will be their product.
If you know that two numbers are relatively prime can you predict what the least common multiple will be?
The least common multiple of two numbers is the product of those two numbers, divided by the greatest common factor of those two numbers. Two numbers that are relatively prime have a greatest common factor of 1. So, when the two numbers are relatively prime, the least common multiple is the product of both numbers divided by 1. So, when two numbers are relatively prime, the least common multiple is the product of the two numbers.this is wron
Is it true that the Least Common Multiple of two numbers is equal to their product divided by their Greatest Common Factor?
Yes.
What is the the greatest common multiple of any two numbers?
There is no "greatest common multiple" of any two numbers. Whatever their product is, it can be multiplied by any positive integer to yield an even greater number that is also a multiple of the first two. Thus, the number of multiples is infinite.
