If the product of two numbers is 324 and their H.C.F. is 3, then their L.C.M. will be

### Concept & Formula The relationship between the Highest Common Factor (H.C.F.), Lowest Common Multiple (L.C.M.), and the product of two numbers is constant. $$ \text{Product of Two Numbers} = \text{H.C.F.} \times \text{L.C.M.} $$ ### Step-by-Step Solution * **Given:** * Product of the two numbers = 324 * H.C.F. = 3 * Let the required L.C.M. be $L$. * Substitute the given values directly into the standard formula: $324 = 3 \times L$. * Solve for $L$: $L = \frac{324}{3}$. * Perform the division: $324 / 3 = 108$. ### Exam Strategy & Shortcut This is a direct application of the formula and requires minimal calculation. To speed it up mentally, break down 324 into $300 + 24$. Dividing by 3 gives you $100 + 8 = 108$. You should solve this entirely in your head within 5 seconds without touching pen to paper. ### Common Pitfall A common trap for students rushing through the exam is misreading "product of two numbers" as one of the numbers, leading them to multiply 324 by 3 (yielding 972, which is cleverly placed as option a). Always pause for one second to ensure you've correctly identified whether you are given the individual numbers or their total product. ### Final Answer **Therefore, the correct answer is 108.**