Aishwarya1204 wrote:Just wanted to confirm, if we know the GCF and LCM of two numbers, we can only find out the product of 2 numbers and not the actual values of the 2 numbers right?
The only rule I came across regarding this is:
GCF of 2 numbers * LCM of two numbers = the product of the 2 numbers !
Hmm, I think this answer is . . . sometimes yes and sometimes no.
For example, if the GCF of x and y is 2, and the LCM of x and y is 12, then we can conclude that xy = (2)(12) = 24. In this case, the numbers could be 4 and 6,
or the numbers could be 2 and 12
Conversely, if the GCF of x and y is 3, and the LCM of x and y is 24, then we can conclude that xy = (3)(24) = 72. In this case, the numbers
must be 3 and 24
So, the million dollar question is, "Under what circumstances does our rule indicate only one pair of numbers?"
I'm not too sure about that. However, I am quite certain that I've never seen an official GMAT test this rule. Although I have seen some advanced questions test the rule that says,
"If the GCF of x and y is m, and if the LCM of x and y is n, then xy = mn"
Cheers,
Brent
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