Discussion
The ratio of two numbers is 3 : 7 and their LCM is 630. Then, sum of the LCM and HCF of these numbers is :
Answer: D
The sum of the LCM and HCF is 660.
Let the numbers be 3k and 7k, where k is their HCF, since 3 and 7 are co-prime:
\[ \begin{aligned} \text{LCM} &= 3 \times 7 \times k = 21k = 630 \\ k &= 30 = \text{HCF} \\ \text{LCM} + \text{HCF} &= 630 + 30 = 660 \end{aligned} \]
The numbers are 90 and 210. 30 is the HCF alone, and 600 is the difference rather than the sum.
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