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
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