If a and b are positive integers, what is the value of the product ab?

Question

If a and b are positive integers, what is the value of the product ab ?

(1) The least common multiple of a and b is 48.

(2) The greatest common factor of a and b is 4.

chetan2u · Accepted Answer

Whenever a Q talks of product, LCM and HCF of two numbers .............  most likely it will deal with the formula..  
 Product = LCM * HCF

the two statements give LCM and HCF separately ..
 so COMBINED we can get the product as 48*4 
suff
C

BrentGMATPrepNow · Answer

Target question :    What is the value of the product ab?

Statement 1 : The least common multiple of a and b is 48  
Let's TEST some numbers. 
There are several values of a and b that satisfy statement 1. Here are two: 
 Case a : a = 1 and b = 48. In this case,  ab = (1)(48) = 48 
 Case b : a = 2 and b = 48. In this case,  ab = (2)(48) = 96 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The greatest common factor (aka divisor) of a and b is 4 
Let's TEST some numbers (again). 
There are several values of a and b that satisfy statement 2. Here are two: 
 Case a : a = 8 and b = 4. In this case,  ab = (8)(4) = 32 
 Case b : a = 4 and b = 4. In this case,  ab = (4)(4) = 16 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
--------ASIDE----------------------
There's a nice rule that says:
  (greatest common divisor of x and y)(least common multiple of x and y) = xy  
 Example : x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above   rule  , since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

When we apply the above   rule  , we get: (4)(48) = ab
So,  ab = 192 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

hasnain3047 · Answer

(GCF)(LCM)=Product
So
From statemnt 1 we get LCM and from statement 2 we get GCF.
So ab=48*4

Hence Answer is C

Posted from my mobile device

LeoN88 · Answer

LCM(a,b) * HCF(a*b) = a*b

Option  C

LLM1500 · Answer

re:

Case b: a = 2 and b = 48. In this case, ab = (2)(48) = 96

Isnt' the least common multiple of 2 and 48 -> 48?

ScottTargetTestPrep · Answer

Solution:
 
We need to determine the value of the product ab, given that a and b are positive integers.

Statement One Alone:

Knowing that the least common multiple (LCM) of a and b is 48 is not sufficient. For example, if a = 1 and b = 48, then ab = 48. However, if a = 2 and b = 48, then ab = 96.

Statement Two Alone:
 
Knowing that the greatest common factor (GCF) of a and b is 4 is not sufficient. For example, if a = 4 and b = 8, then ab = 32. However, if a = 4 and b = 12, then ab = 48.

Statements One and Two Together: 
 
Knowing both values of the LCM and GCF of a and is sufficient since we have a formula that relates the two:

LCM(a, b) * GCF(a, b) = a * b

Therefore, ab = 48 * 4 = 192.

Answer: C

yannichc · Answer

Yes - but you want AB to be the same

a=1 b = 48 --> LCM = 48 and ab= 48

if your replace a=1 with a=2 then ab becomes 96

jaykayes · Answer

Is the rule valid for any quantity of numbers?
In other words, will (HCF of a,b,c, ...n) X (LCM of a,b,c, ...n) = a X b X c X ....n?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a and b are positive integers, what is the value of the product ab?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If a and b are positive integers, what is the value of the product ab?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards