The least common multiple of positive integers p and q is 72. What is

Question

The least common multiple of positive integers p and q is 72. What is the greatest common factor of p and q?

(1) pq is a perfect square
(2) pq is a perfect fourth power

GMATinsight · Answer

PROPERTY :
 LCM x HCF = Product of those two numbers

ie. p*q = 72*HCF

Question : GCD (HCF) = ? OR p*q = ?

Statement 1 : p*q is a perfect square

i.e. p*q is a multiple of 72 and a perfect square as well

i.e. p*q = {144, 576, 1296... etc}

i.e. GCD = p*q/LCM = {144/72, 576/72, 1296/72... } = {2, 8, 18...}

Multiple possible values hence

NOT SUFFICIENT

Statement 2 : pq is a perfect fourth power

i.e. p*q is a multiple of 72 and a perfect forth power

i.e. p*q = { 1296, 1296*2^4 , ... etc.}

i.e. GCD = p*q/LCM = { 1296/72 ,  1296*2^4/72 ... etc } = {18, 288.. etc.}

BUT GCD can NOT be greater than LCM hence only possible value of GCD = 18

SUFFICIENT

Answer: Option B

Freddy12 · Answer

How do you come up with numbers like 1296 on the spot? Did you choose 1296 as it's 6^4?
Can you explain the logic behind choosing 1296?

anjalic2503 · Answer

pq is multiple of 72 and 72 = 2^3 * 3^2 so in order to get the first perfect forth power we need 2^4 * 3^4 which gives 1296

SirSanguine · Answer

anjalic2503  
You are right! Please use "quote" or "mention" feature when replying to a particular user..this helps them by sending them a notification.

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The least common multiple of positive integers p and q is 72. What is

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