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The HCF of two whole numbers is 8. Which of these can NOT be their LCM?

Competition practiceNumber & Arithmetic
  • A24
  • B60
  • C48
  • D120

Step-by-Step Solution

The HCF always divides the LCM, because both numbers are multiples of the HCF and the LCM is a multiple of both numbers. So the LCM must be a multiple of 8, and 60 ÷ 8 = 7.5 is not whole. The other three are genuinely reachable: 8 and 24 give HCF 8 and LCM 24; 16 and 24 give HCF 8 and LCM 48; 24 and 40 give HCF 8 and LCM 120. What makes 60 tempting is that it IS a multiple of 4, so it passes a half-remembered version of the rule — the test has to use the whole HCF, not one of its factors.
Answer: B) 60

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