Question
Download Solution PDFदो संख्याओं का महत्तम समापवर्तक 9 है और उनका लघुतम समापवर्त्य 252 है। तो संख्याओं का योग क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
म.स. = 9, ल.स. = 252
संकल्पना:
ल.स. = लघुतम समापवर्त्य (न्यूनतम मान सभी दी गयी संख्या द्वारा विभाज्य है)
म.स. = महत्तम समापवर्तक (उच्चतम मान जो पूर्ण रूप से सभी दी गयी संख्याओं को विभाजित करेगा)
प्रयोग किया गया सूत्र:
ल.स. × म.स. = संख्याओं का गुणनफल
गणना:
माना कि संख्याएँ 9x और 9y हैं जहाँ x और y सह-अभाज्य हैं।
प्रश्नानुसार,
9x × 9y = 252 × 9
⇒ xy = 28
(x, y) के संभव मान (1, 28), (28, 1), (4, 7) और (7, 4) हैं।
स्थिति 1: (x, y) के लिए (1, 28) या (28, 1) है।
संख्याएँ = (9 × 1) = 9 और (9 × 28) = 252 हैं।
⇒ संख्याओं का योग = (9 + 252) = 261
स्थिति 2: (x, y) के लिए (4, 7) या (7, 4) है।
संख्याएँ = (9 × 4) = 36 और (9 × 7) = 63 हैं।
⇒ संख्याओं का योग = (36 + 63) = 99
∵ 261 विकल्पों में नहीं है,
∴ आवश्यक योग = 99
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