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Q: Write a program to accept 2 numbers and tell whether the product of the two number is equal to or greater than 1000?

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If their GCF is 1, their LCM is their product. If their GCF is greater than 1, their LCM is less than their product.

If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.

Given any number, there is an even number that exists greater than it. That even number is a product: of 2 and some number. Therefore, the number that you started with is less than the product of a pair of numbers.

If the two numbers have no prime factors in common, their LCM will be their product. If there are prime factors in common, their LCM will be less than their product.

Comparison

By finding out whether they have any factors in common. If the only factor they have in common is 1, the LCM will be their product. If they have more factors in common, their LCM will be less than their product.

Compare numbers.

If none of the prime factors are in common, the LCM will be the product of the two.

If the two numbers have no common factors other than 1, the LCM will be their product. If there are other common factors, the LCM will be less.

If they have no common factors other than 1.

If the prime factorizations have no factors in common, the LCM is the product of them.

If there are no prime factors in common, the LCM will be the product. If there are prime factors in common, the LCM will be less than the product.

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