दो संख्याओं का HCF 12 है। निम्नलिखित में से कौन-सा उनका LCM कभी नहीं हो सकता है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)
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  1. 72
  2. 60
  3. 90
  4. 84

Answer (Detailed Solution Below)

Option 3 : 90
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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दिया 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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