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Every time I've seen a similar question, one of the numbers is a multiple of the other and the two numbers satisfy the requirements. 9 and 54 have a GCF of 9 and an LCM of 54.

Another way to solve it: The product of the GCF and LCM of two numbers is equal to the product of the two numbers. 9 x 54 = 486. Now you're looking for another factor pair of 486 that satisfy those requirements. 18 and 27 do that.

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If p and q are any two coprime factors of LCM/GCF = 6, then p*GCF and q*GCF will be an answer.

So two possible pair of answers are obtained by (p,q) = (1, 6) and (2, 3)

And the answers are: (, 54) and (18, 27).

Q: How did you find a pair of numbers whose GCF is 9 and whose LCM is 54?

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The product of the GCF and the LCM of two numbers is equal to the product of the original two numbers. Multiply the GCF and the LCM. The original two numbers will be another factor pair of that total. Find the factor pair that has that GCF and LCM.

The pair of numbers whose GCF is 1 and LCM is 36 is 9 and 4. The numbers should be greater than their GCF and less than their LCM.

Numbers whose GCF is 1, like 24 and 49, are known as relatively prime. This means that they have no prime factors in common.

The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.

Any pair of prime numbers as for example 19 and 23

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A number pair whose GCF is the same as one of the numbers is i , i x j where i and j are integers greater than zero. If i=3 and j=5 then the number pair will be 3,15. The GCF is 3. If i=7 and j=11 the number pair will be 7,77 and the GCF 7. The number of possible solutions is infinite.

The product of the GCF and the LCM of two numbers is equal to the product of the original two numbers. Multiply the GCF and the LCM. The original two numbers will be another factor pair of that total. Find the factor pair that has that GCF and LCM.

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the two smallest numbers are 49 and 14

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