Discussion
If HCF of two numbers is 18, then which of the following cannot be their LCM ?
Answer: A
The impossible LCM is 128.
The HCF of two numbers always divides their LCM, so the LCM must be a multiple of 18.
\[ \begin{aligned} 108 &= 18 \times 6, \quad 72 = 18 \times 4 \\ 144 &= 18 \times 8, \quad 128 \div 18 \approx 7.11 \end{aligned} \]
108, 72 and 144 are multiples of 18, so each could be the LCM (for example 18 and 108, 18 and 72, 18 and 144). 128 is not even divisible by 9, so it cannot be a multiple of 18 and cannot be their LCM.
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