Discussion
The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other number is
Answer: B
The other number is 308.
For any two numbers, the product of the numbers equals the product of their HCF and LCM:
\[ \begin{aligned} 275 \times n &= 11 \times 7700 \\ n &= \frac{84700}{275} = 308 \end{aligned} \]
Check: \(275 = 11 \times 25\) and \(308 = 11 \times 28\). Since 25 and 28 share no factor, the HCF is 11 and the LCM is \(11 \times 25 \times 28 = 7700\). 28 is the cofactor of 308 after removing the HCF, and 700 and 37 are not multiples of 11, so they cannot have an HCF of 11 with 275.
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