LCM GCF

[kop]

The Least Common Multiple of three numbers is four times their Greatest Common Factor. Which of the following must be true of the numbers?

I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as Greatest Common Factor.

[theCodeToGMAT]

A = (GCD) * _
B = (GCD) * _
C = (GCD) * _

LCM = 4 * GCD

A = (GCD)
B = (GCD) * (2)
C = (GCD) * (2)^2

Or
A = (GCD)
B = (GCD)
C = (GCD) * (2)^2

Or
A = (GCD)
B = (GCD) * (2)^2
C = (GCD) * (2)^2

I. At least one of the numbers is odd.
--> No

II. Two of the three numbers must be same.
--> "must" - NO

III. At least one number is the same as Greatest Common Factor.
--> YES

So, (III)

Is it the answer?

[[email protected]]

Hi kop,

In Roman Numeral questions, it's important to have the answer choices as reference. The way the answers are written will likely allow you to "skip" some of the math (and not have to deal with all 3 Roman Numerals). It's also worth noting that it's easier to prove what's NOT TRUE in these types of situations.

I. At least 1 is odd.

If we use 2, 2, and 8 then the LCM is 4 times the GCF.
Roman Numeral 1 is NOT TRUE

II. Two of the three numbers must be the same.

If we use 1, 2 and 4, then the LCM is 4 times the GCF
Roman Numeral 2 is NOT TRUE

III. At least one of the numbers = the GCF

I can't seem to find a way to eliminate this one, so I assume that it's true.

GMAT assassins aren't born, they're made,
Rich

[Mathsbuddy]

This is what I reckon:

3 values A, B, C must be composed of factors a, b, c and F:

A = 2 * a * F
B = 2 * b * F
C = 1 * c * F

where F = highest common factor

LCM = 4F, therefore a = b = c = 1

So,

A = 2 * F
B = 2 * F
C = 1 * F

I. At least one of the numbers is odd - Not necessarily as F can be odd or even.
II. Two of the three numbers must be same - True (A and B)
III. At least one number is the same as Greatest Common Factor - True (C)

[Mathsbuddy]

CORRECTION:

I stand corrected by counter examples!

[[email protected]]

Hi Mathsbuddy,

In Quant questions that ask for "what MUST be true", you have to be thorough enough to prove what "COULD be true" vs. what "MUST be true." That difference will be the difference between getting the question right and getting it wrong.

GMAT assassins aren't born, they're made,
Rich