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Which of the following pairs of numbers has HCF 14 and LCM 210?

Class 10HCF and LCMNumber Systems
  • A28 and 105
  • B56 and 70
  • C42 and 105
  • D42 and 70

Step-by-Step Solution

Write the numbers as and with a, co-prime; then LCM = gives , so (a, b) = (3, 5) or (1, 15). The pair 42 and 70 fits: HCF = 14, LCM = 210, and . Watch the near-misses - 42 and 105 have the right LCM (210) but HCF 21, while 56 and 70 have the right HCF (14) but LCM 280; 28 and 105 give HCF 7 and LCM 420.
Answer: D) 42 and 70

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