The least common multiple (LCM) of two positive numbers is 13 times their highest common factor (HCF). The sum of the HCF and LCM is 252. If one of the numbers is 54, find the other number.
The least common multiple (LCM) of two positive numbers is 13 times their highest common factor (HCF). The sum of the HCF and LCM is 252. If one of the numbers is 54, find the other number.
दो धनात्मक संख्याओं का लघुत्तम समापवर्त्य (LCM) उनके महत्तम समापर्वतक (HCF) का 13 गुना है। HCF और LCM का योग 252 हैं।
यदि उनमें से एक संख्या 54 है, तो दूसरी संख्या ज्ञात करें।
Detailed Solution & Logic
78
Let the HCF be $x$.
Then LCM $= 13x$
Given,
$x + 13x = 252$
$14x = 252$
$x = 18$
So,
HCF $= 18$
LCM $= 13 \times 18 = 234$
Using the relation:
Product of two numbers
$= \text{HCF} \times \text{LCM}$
$= 18 \times 234$
$= 4212$
One number is 54.
Let the other number be $n$.
$54 \times n = 4212$
$n = \frac{4212}{54}$
$n = 78$
Correct Answer: 78
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