Question: If p#q denotes the least common multiple of p and q, then ((12#16)#(18#24)) = ?

(A) 216
(B) 180
(C) 144
(D) 108
(E) 72

“If p#q denotes the least common multiple of p and q, then ((12#16)”- is a topic of the GMAT Quantitative reasoning section of GMAT. The question is taken from the book “The Official Guide for GMAT Review.”To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
The most efficient method is to use the Greatest Common Factor: (A * B) / (GCF A&B) = LCM A&B
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So, ((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144

Correct Answer: C

Approach Solution 2:
LCM of 12,16,18 and 24

2^2×3,2^4,2×3^2,2^3×3
= 2^4× 3^2
=144

Correct Answer: C

Suggested GMAT Problem Solving Questions

• In the Decimal Notation of Number (2/23)^3. What is the Third Digit GMAT Problem Solving
• Tom Read a Book Containing 480 Pages by Reading the Same Number GMAT Problem Solving
• A 100-litre Mixture of Milk and Water Contains 36 litres of Milk GMAT Problem Solving
• The Figure shows the Graph of y = (x + 1)(x - 1)^2 in the xy-plane GMAT Problem Solving
• On the Graph above, When x = 1/2, y = 2; and when x = 1, y = 1 GMAT Problem Solving
• A Box Contains 100 Balls, Numbered From 1 To 100 GMAT Problem Solving
• A Hall Is 15 M Long And 12 M Broad GMAT Problem Solving
• The Speed Of A Car Increases By 2 Kms After Every One Hour GMAT Problem Solving
• The Vertices Of A Rectangle In The Standard (X,Y) Coordinate Place Are GMAT Problem Solving
• For Any Positive Integer N, The Sum Of The First N Positive Integers GMAT Problem Solving
• What is the Sum of the First 100 Positive Odd Numbers? GMAT Problem Solving
• A Rectangle is Inscribed in a Circle of Radius r. If the Rectangle is GMAT Problem Solving
• What Is The Remainder When 25^25 Is Divisible By 26 GMAT Problem Solving
• A Quality Control Analyst Collected 200 Measurements Of Length GMAT Problem Solving
• 1/2 + 1/3 + 1/4 + 1/5 + 1/6 GMAT Problem Solving
• A Thief Steals a Car at 2.30 p.m. and Drives it at 60 km/h. The Theft GMAT Problem Solving
• If |x + 1 | > 2x - 1, Which Of The Following Represents The Correct Range GMAT Problem Solving
• Which Of The Following Is A True Statement? GMAT Problem Solving
• A machine puts c caps on bottles in m minutes. How many hours will it GMAT Problem Solving
• What is the least common multiple of 15, 18, and 24? GMAT Problem Solving