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HCF & LCM
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NTPC Graduate Tier 1 2016 Shift 2 📅 02 Apr, 2016

The HCF and LCM of two numbers are 3 and 2730 respectively. If one of the numbers is 78, find the other number.

A
107
B
103
C
105
D
102
Result Summary
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NTPC Graduate Tier 1
2016 • 02 Apr, 2016 • Shift 2
The HCF and LCM of two numbers are 3 and 2730 respectively. If one of the numbers is 78, find the other number.
Correct Answer
105
Core Mathematical Theorem: In number theory, there is a fundamental rule that applies to any two positive integers: The product of the two numbers is always exa......
Ref/Book : NTPC Graduate Tier 1 2016
Ref. Subject Number System
Chapter -
Ref. Topic HCF & LCM
Pg. No -
💡 Analysis & Explanation
Core Mathematical Theorem ▼
In number theory, there is a fundamental rule that applies to any two positive integers: The product of the two numbers is always exactly equal to the product of their Highest Common Factor (HCF) and Least Common Multiple (LCM). Formula: Number1 * Number2 = HCF * LCM.
Data Substitution ▼
Applying the given values into the formula yields: 78 * Number2 = 3 * 2730.
Arithmetic Execution ▼
Number2 = (3 * 2730) / 78. Simplifying this, Number2 = 8190 / 78.
Final Result ▼
Performing the division gives exactly 105.
Conclusion ▼
The second unknown number is mathematically proven to be 105.
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