Allied & ICAR Exam Bank • ALLIED_2491NAT • 2 Marks
Section 8: General Aptitude
Quantitative Aptitude
Subtopic: Numerical Computation
Question Statement:
The number of pairs of positive integers having HCF = 16 and LCM = 480 is:
Answer Key:
4
Step-by-Step Solution & Explanation
Let numbers be $16a$ and $16b$ where $\gcd(a, b) = 1$. LCM = $16ab = 480 \implies ab = 30$. Coprime pairs $(a, b)$ with $a < b$: $(1, 30), (2, 15), (3, 10), (5, 6)$. There are 4 pairs.