The LCM of three different numbers is 1024. Which one of the following can…
2024
The LCM of three different numbers is 1024. Which one of the following can never be there HCF?
- A.
8
- B.
124
- C.
32
- D.
256
Attempted by 112 students.
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Correct answer: B
Key idea: The LCM is 1024 = 2^10, so all three numbers can only have 2 as a prime factor. Therefore the HCF must be a divisor of 1024 and must be a power of 2.
8 can be the HCF. Example: 8, 16, and 1024 have HCF 8 and LCM 1024.
32 can be the HCF. Example: 32, 64, and 1024 have HCF 32 and LCM 1024.
256 can be the HCF. Example: 256, 512, and 1024 have HCF 256 and LCM 1024.
124 cannot be the HCF. Since 124 = 4 × 31 includes the prime 31 which does not divide 1024, it cannot be a common factor of numbers whose LCM has only the prime 2.
Conclusion: 124 can never be the HCF.