Product of two co-prime numbers is 117. Their L.C.M. should be

### Concept & Rule Co-prime numbers (or relatively prime numbers) are a pair of numbers that share absolutely no common positive factors other than 1. Consequently, their Highest Common Factor (H.C.F.) is exactly 1. $$ \text{For co-prime numbers } a \text{ and } b, \text{ L.C.M.}(a,b) = a \times b $$ ### Step-by-Step Solution * **Given:** The numbers are co-prime, and their product is 117. * By the mathematical definition of co-prime numbers, their H.C.F. must be 1. * Using the standard relationship formula: * $\text{Product of Numbers} = \text{H.C.F.} \times \text{L.C.M.}$ * Substitute the known variables into the equation: * $117 = 1 \times \text{L.C.M.}$ * Therefore, the L.C.M. is simply 117. ### Exam Strategy & Shortcut This question tests pure conceptual knowledge and requires zero calculation. If you see the term "co-prime" and are asked for the L.C.M., instantly select the product provided in the prompt. Do not waste time trying to factorize the number. ### Common Pitfall Students who forget the definition of "co-prime" often attempt to factorize 117 (into $9 \times 13$) and get bogged down looking for missing information. Others might select "cannot be calculated" out of confusion. Trust the definitions of number properties. ### Final Answer **Therefore, the correct answer is 117.**