The LCM of two co-prime numbers is 117. What is the sum of squares of the…

Answer: 250

Explanation:

• For coprime numbers, LCM = product, so if the numbers are a and b with gcd(a,b) = 1 then a × b = 117.

• Prime factorization: 117 = 3 × 3 × 13 = 9 × 13.

• Possible positive factor pairs of 117 are (1, 117), (3, 39), and (9, 13). Among these, (1, 117) and (9, 13) are coprime; (3, 39) is not coprime.

• Compute sums of squares: 1^2 + 117^2 = 13690 (not an option); 3^2 + 39^2 = 1530 (but 3 and 39 are not coprime); 9^2 + 13^2 = 81 + 169 = 250.

• Therefore the valid coprime pair giving a choice in the options is 9 and 13, and the required sum of squares is 250.