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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.

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βˆ™ 2012-10-27 12:55:58
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Q: Why is the product of the LCM and HCF the same as the product of the original pair of numbers?
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Related questions

Which product has a factor pair in which both numbers are the same?

A square 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.


How are the sum and product of each pair of numbers related?

They have the same parity (odd or even).


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What do you mean by product?

The product of numbers is the same as the multiplication of numbers


What is a product of the same two numbers?

The product of the same two numbers, is the number's square.


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


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The product of the GCF and LCM of two numbers is the same as the product of the numbers.


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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.


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