Two numbers have an H.C.F of 8. Which of the following cannot be their L.C.M?
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Answer: D. 60
Explanation
A fundamental property of number theory states that the lowest common multiple of two numbers must always be exactly divisible by their highest common factor. Checking the given options against the HCF of eight shows that twenty-four, forty-eight, and fifty-six are all perfectly divisible by eight. Sixty is not divisible by eight without a remainder, making sixty impossible as a valid LCM for these numbers. The HCF is a factor of both numbers, and since both numbers must divide evenly into their LCM, the HCF must also divide evenly into the LCM. Divisibility rules for eight require that a number's factors must include three powers of two. Number theory constraints allow us to eliminate impossible answer choices without knowing the exact original numbers.
Option A is divisible by eight, making it a valid potential LCM for two numbers with an HCF of eight. Option B is a valid multiple of eight and can easily serve as the LCM for numbers like sixteen and twenty-four. Option C is divisible by eight seven times, qualifying it as a mathematically possible LCM.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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