Discussion
The LCM of three different numbers is 120. Which of the following cannot be their HCF?
Answer: D
The HCF of numbers always divides their LCM, so any HCF of three numbers whose LCM is 120 must be a factor of 120. 8, 12 and 24 are factors of 120, but 35 is not (120 / 35 is not a whole number).
So 35 cannot be their HCF, option D.
The same test applies to LCM and HCF whatever the numbers: the HCF is a divisor of every number and the LCM is a multiple of every number, so the HCF must divide the LCM. The divisors of 120 include 8, 12 and 24, but 35 contains the factor 7, which 120 does not have.
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