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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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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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No, multiplying a set of numbers can only come out as one product. Therefore, two numbers having the same prime factorization is impossible.

2 x 14 = 28 3 x 7 = 21 They do not appear to be the same product.

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.

It's a square number. Square numbers have a factor pair that is the same number twice. When listed, that number occurs once.

The numbers 2, 14, 3 and 7 are all factors of 42 because 42 is their lowest common multiple

Related questions

A square number

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.

They have the same parity (odd or even).

2 and 2

The same as the product of the original numbers, 1440.

Only if the magnitudes of two numbers are the same.

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

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

the least common multiple of 5 and 6 is 30 and 30 is the product of 5*6

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

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.

Yes.

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