Directions: Solve the number series to answer the following questions. $\sqrt[n]{A}$, 31, B, C, 439, B + 687, 1296 Note: (i) All the terms in the given series and 'n' are positive integer. (ii) Difference between 31 and B is X, which has 3 factors excluding X itself, those are 13, 5 and (A - 8). What is the LCM of $(B + 34)$ and $X$?

### Concept & Least Common Multiple (LCM) Once the variables from the series conditions are resolved, calculating the LCM involves finding the smallest positive integer that is perfectly divisible by both numbers. ### Step-by-Step Solution 1. **Retrieve previously solved variables:** From decoding the series conditions in the previous step, we know the difference $X = 65$ and the series term $B = 96$. 2. **Substitute into the expression:** We need to find the LCM of $(B + 34)$ and $X$. 3. Calculate $(B + 34) = 96 + 34 = 130$. 4. Now, find the Least Common Multiple (LCM) of 130 and 65. 5. Since 130 is a direct multiple of 65 ($65 \times 2 = 130$), the smallest number perfectly divisible by both is 130 itself. ### Exam Strategy & Shortcut Always check if the larger number is a multiple of the smaller number before using prime factorization trees or division methods. If $Y$ is a multiple of $X$, then $\text{LCM}(X, Y) = Y$. This skips unnecessary calculation steps. ### Common Pitfall A common mistake is simply multiplying both numbers together to find the LCM, which yields $130 \times 65 = 8450$. This is a common multiple, but absolutely not the *least* common multiple. ### Final Answer Therefore, the correct answer is **130**.