दो संख्याएँ 6 ∶ 5 के अनुपात में हैं। यदि उनका HCF 3 है, तो दोनों संख्याओं का LCM क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 3)
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  1. 64
  2. 110
  3. 90
  4. 80

Answer (Detailed Solution Below)

Option 3 : 90
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दिया गया है:

दो संख्याएँ 6 ∶ 5 के अनुपात में हैं।

उनका HCF 3 है।

प्रयुक्त अवधारणा:

1. यदि P, A और B का HCF है, तो A = P × m और B = P × n है। (जहाँ m और n कोई भी धनात्मक पूर्णांक हैं और वे एक-दूसरे के सह-अभाज्य हैं)

2. LCM दो या दो से अधिक संख्याओं का न्यूनतम उभयनिष्ठ गुणज होता है।

गणना:

पहली संख्या = 6 × 3 = 18

दूसरी संख्या = 5 × 3 = 15

LCM (18, 15) = 3 × 6 × 5 = 90

∴ उनका LCM 90 है।

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