Question
Download Solution PDFयदि दो संख्याओं का अनुपात 17 : 7 है तथा उनके लघुत्तम समापवर्त्य (LCM) और महत्तम समापवर्तक (HCF) का गुणनफल 119 है, तो उनके LCM और HCF के व्युत्क्रमों का योग है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
दो संख्याओं का अनुपात 17:7 है।
उनके LCM और HCF का गुणनफल 119 है।
प्रयुक्त सूत्र:
दो संख्याओं का गुणनफल = LCM × HCF
LCM और HCF के व्युत्क्रमों का योग = (1/LCM) + (1/HCF)
गणना:
मान लीजिए दो संख्याएँ 17x और 7x हैं।
दो संख्याओं का गुणनफल = 17x × 7x = 119x²
⇒ LCM × HCF = 119
LCM × HCF = दो संख्याओं का गुणनफल
⇒ 119x² = 119
⇒ x² = 1
⇒ x = 1
⇒ संख्याएँ हैं 17x = 17 और 7x = 7
17 और 7 का LCM = 119
17 और 7 का HCF = 1
LCM और HCF के व्युत्क्रमों का योग = (1/LCM) + (1/HCF)
⇒ योग = (1/119) + (1/1)
⇒ योग = 120/119
∴ सही उत्तर विकल्प (3) है।
Last updated on Jul 17, 2025
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