2, 3, 5, 6, 9 और 18 से विभाज्य वह न्यूनतम संख्या ज्ञात कीजिए, जो एक पूर्ण वर्ग है।

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 2)
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  1. 900
  2. 400
  3. 144
  4. 3600

Answer (Detailed Solution Below)

Option 1 : 900
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SSC CGL Tier 1 2025 Full Test - 01
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प्रयुक्त अवधारणा:

सबसे छोटी पूर्ण वर्ग संख्या ज्ञात करना जो 2, 3, 5, 6, 9 और 18 से विभाज्य है।

सबसे पहले, दी गई संख्याओं का लघुत्तम समापवर्त्य (LCM) ज्ञात कीजिए।

गणना

LCM (2, 3, 5, 6, 9 और 18) = 90

90 = 2 × 3 × 3 × 5

क्योंकि LCM के गुणनखंड में 2 और 5 जोड़ी में नहीं हैं, इसलिए इसे एक पूर्ण वर्ग बनाने के लिए हमें 90 को 5 और 2 से गुणा करना होगा।

90 × 2 × 5 = 900

∴ 2, 3, 5, 6, 9 और 18 से विभाज्य न्यूनतम पूर्ण वर्ग संख्या 900 है।

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