सबसे छोटी प्राकृतिक संख्या जो 26, 20, 40 और 13 से विभाज्य है:

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OSSC Excise SI (Mains) Official Paper (Held On: 17 Oct, 2024 Shift 2)
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  1. 538
  2. 442
  3. 545
  4. 520

Answer (Detailed Solution Below)

Option 4 : 520

Detailed Solution

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दिया गया:

संख्याएँ हैं: 26, 20, 40, 13

प्रयुक्त सूत्र:

इन संख्याओं से विभाज्य सबसे छोटी संख्या ज्ञात करने के लिए हमें LCM (लघुत्तम समापवर्त्य) की गणना करनी होगी।

गणना:

अभाज्य गुणनखंड:

26 = 2 × 13

20 = 2² × 5

40 = 2³ × 5

13 = 13

LCM = प्रत्येक अभाज्य गुणनखंड की उच्चतम घात:

एल.सी.एम. = 2³ × 5 × 13 = 8 × 5 × 13 = 520

∴ 26, 20, 40 और 13 से विभाज्य सबसे छोटी प्राकृतिक संख्या 520 है।

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