PYQ · UPSC Combined Defence Services 2022 · Elementary Mathematics · Q5 Difficulty 3/5
Number System & Relations Between Numbers› HCF, LCM & Factors
Suppose p and q are the LCM and HCF respectively of two positive numbers. If p : q = 14 : 1 and pq = 1134, then what is the difference between the two numbers?
Answer d.
Explanation Answer · d
Two coprime reduced pairs yield different differences, so the data do not fix one answer. Let HCF=q and LCM=14q. Their product gives 14q²=1134, so q=9 and LCM=126. Coprime reduced pairs can be (1,14) or (2,7), giving numbers (9,126) or (18,63), with differences 117 and 45. The difference is not unique.
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