Discussion
The Highest Comon Factor (HCF) of two numbers is 11 and their Least Common Factor (LCM) is 693. If one of the numbers is 77, then the other number is:
Answer: B
The other number is 99.
For two numbers, the product of the numbers equals the product of their HCF and LCM.
\[ \begin{aligned} 77 \times n &= 11 \times 693 \\ n &= \frac{7623}{77} = 99 \end{aligned} \]
Check: \(77 = 7 \times 11\) and \(99 = 9 \times 11\), so their HCF is 11 and their LCM is \(7 \times 9 \times 11 = 693\). 33 also shares the factor 11 with 77, but its LCM with 77 is 231, not 693. 96 and 89 are not multiples of 11, so they cannot have 11 as a common factor with 77.
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