LCM and GCF

[Aishwarya1204]

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 !

[Brent@GMATPrepNow]

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

[Aishwarya1204]

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

Thank you so much !

Yeah that is what I was wondering, because I saw a data sufficiency question which had the question stem asking to identify the two numbers and in the statements it had the LCM of the 2 numbers in one of them and GCF in the other, and the answer was C !

But good to know that it isnt that important from the point of view of the actual GMAT. .

[anuprajan5]

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

Brent,

I assume that if either the LCM or the GCF is 1 prime number, then you can determine x or y.

REgards
Anup