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For some pair of whole numbers, which of the following could be the HCF and the LCM?

Competition practiceNumber & Arithmetic
  • AHCF 16 and LCM 380
  • BHCF 24 and LCM 540
  • CHCF 15 and LCM 175
  • DHCF 18 and LCM 378

Step-by-Step Solution

The HCF divides both numbers, and both numbers divide the LCM, so the HCF must always divide the LCM exactly. Testing: 380 ÷ 16 = 23.75, 540 ÷ 24 = 22.5 and 175 ÷ 15 = 11.67 all fail, but 378 ÷ 18 = 21 works. A genuine pair is 54 and 126, whose HCF is 18 and LCM is 378. Swapping the roles of HCF and LCM — asking whether the LCM divides the HCF — is the usual confusion.
Answer: D) HCF 18 and LCM 378

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