Question
Download Solution PDFदो संख्याओं का HCF 12 है। निम्नलिखित में से कौन-सा उनका LCM कभी नहीं हो सकता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
दो संख्याओं का HCF 12 है।
प्रयुक्त अवधारणा:
1. यदि P, A और B का HCF है, तो A = P × m और B = P × n
2. LCM दो या दो से अधिक संख्याओं का लघुतम समापवर्त्य है।
गणना:
मान लीजिये, दो संख्याओं का अनुपात A : B है और उनका HCF H और LCM L है।
फिर, संख्याएँ क्रमशः AH और BH हैं।
LCM (AH, BH) अर्थात् L = H × A × B
अतः, L, H का गुणज है।
इसलिए, यदि दो संख्याओं का HCF 12 है, तो उनका LCM 12 का गुणज होना चाहिए।
अतः, 90 उनका LCM नहीं हो सकता।
∴ 90 उनका LCM कभी नहीं हो सकता।
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