The product of two numbers is 1320 and their H.C.F. is 6. The L.C.M. of the numbers is

### Concept & Formula There is a strict mathematical relationship between the product of two numbers and the product of their H.C.F. and L.C.M. $$ \text{Product of Two Numbers} = \text{H.C.F.} \times \text{L.C.M.} $$ ### Step-by-Step Solution * **Given:** * Product of the numbers = 1320 * H.C.F. = 6 * Substitute these given values directly into the core formula: * $1320 = 6 \times \text{L.C.M.}$ * Isolate the L.C.M. by dividing the total product by the H.C.F.: * $\text{L.C.M.} = \frac{1320}{6}$ * Perform the division: * $1320 / 6 = 220$. ### Exam Strategy & Shortcut Break down the mental division to save time and reduce errors. Split 1320 into easily divisible chunks: $1200 + 120$. Dividing by 6 gives you $200 + 20 = 220$. This technique bypasses the need for long division on paper. ### Common Pitfall A recurring error is failing to read the word "product" and assuming 1320 is just one of the two numbers. This leads students to multiply 1320 by 6 to find a larger L.C.M., resulting in 7920 (option d). Always pause to verify if the question provides individual numbers or their combined product. ### Final Answer **Therefore, the correct answer is 220.**