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Why is the product of the LCM and HCF the same as the product of the original pair of numbers?
It's the way numbers work. Consider 32 and 33. Consecutive integers are relatively prime, that is, their GCF is 1. If two numbers have a GCF of 1, the LCM will be their product.
32 x 33 = 1056
1 (GCF) x 1056 (LCM) = 1056
2 x 528 = 1056
3 x 352 = 1056
4 x 264 = 1056
Notice the pattern. As the GCF increases, the LCM decreases. Consider 32 and 34.
Consecutive even numbers have a GCF of 2. The LCM of 32 and 34 is 544.
32 x 34 = 1088
2 (GCF) x 544 (LCM) = 1088
If you know either the GCF or the LCM of two numbers, you can find the other one without factoring again. The GCF of 28 and 36 is 4. Their product is 1008. Their LCM is 1008 divided by 4, or 252.
What else can I help you with?
Can two numbers have the same prime factorization?
No, multiplying a set of numbers can only come out as one product. Therefore, two numbers having the same prime factorization is impossible.
Find three pairs of numbers for which the LCM equals the product of the two numbers?
Sure thing, honey. Here are three pairs of numbers for you: (1, 1), (2, 2), and (3, 3). In each of these cases, the Least Common Multiple (LCM) equals the product of the two numbers because, well, they're the same darn numbers! It's simple math, darling.
What are the factor pairs of NEGATIVE numbers?
The numbers are the same as positive numbers, just the signs change. Write out the factor pairs as if the number were positive, but make one of the numbers positive and one negative. Now write the same pairs over again and reverse the signs. Negative numbers have twice as many factor pairs as positive numbers do.
Look at the following multiplication sentences 2 14 and 3 7 are these numbers all factors of the same product explain your answer?
2 x 14 = 28 3 x 7 = 21 They do not appear to be the same product.
If the product of two numbers is even then the two numbers must be even right?
Not necessarily, but at least ''one'' of them must be even, unless the two numbers are both the (irrational) square root of the same even number.
How do you change GCF into a LCM with 3 numbers?
The product of the GCF and the LCM is the same as the product of the original two numbers. Divide the product of the original numbers by the GCF. The result will be the LCM.
Which product has a factor pair in which both numbers are the same?
A square number
How are the sum and product of each pair of numbers related?
They have the same parity (odd or even).
What are a pair of whole numbers whose sum is the same as their product?
2 and 2
What is a pair of numbers where the least common multiple is the same as the product of that number?
the least common multiple of 5 and 6 is 30 and 30 is the product of 5*6
When will the greatest common factor of a pair of numbers equal the least common multiple of the same pair of numbers?
Only if the magnitudes of two numbers are the same.
What is a product of the same two numbers?
The product of the same two numbers, is the number's square.
What do you mean by product?
The product of numbers is the same as the multiplication of numbers
How can you know the numbers from their LCM and GCF?
The above is completely true. However, factoring problems in textbooks are usually arranged to have one correct answer. The thing these sorts of problems want you to remember is that the product of the GCF and the LCM of a pair of numbers is the same as the product of the numbers. If you are given the GCF and LCM of a pair of numbers, multiply them together. The numbers will be another factor pair of that product.
Why do some numbers have their LCM and their product the same?
If the two numbers do not have any factors in common (other than 1), then the LCM is the same as the product of the two numbers. Example: LCM of 5 & 6 is 30, which is the same as the product.
How do you work out which 2 numbers have an lcm of 30 and an HCF of 3?
In these types of problems, the numbers can also be the answer. 3 and 30 have a GCF of 3 and an LCM of 30. Since the product of the GCF and LCM of two numbers is the same as the product of the numbers, you could also use another factor pair of 90, like 6 and 15.
Will any pair of prime numbers have the same GCF?
Yes.
