Two numbers are in the ratio $3 : 8$ and their LCM is 432. What is the sum of the two numbers?

Explanation

1. 01

   Let the numbers be 3k and 8k, where k is their HCF.

2. 02

   Since 3 and 8 are co-prime, $\operatorname{LCM} = 3 \times 8 \times k = 24k = 432$, so $k = 18$.

3. 03

   Numbers are 54 and 144. Sum = $54 + 144 = 198$.