### LCM (Least Common Multiple) **Definition:** The smallest positive integer that is a multiple of two or more numbers. **Calculation:** LCM = Common factor of all the three figures AND common factor of two figures (x) Remaining factor of all the figures. Alternatively: LCM = Common factor $\times$ Remaining factor ### HCF or GCD (Highest Common Factor / Greatest Common Divisor) **Definition:** The largest positive integer that divides each of the integers. HCF = Product of only common factors. ### Simple Interest **Key Terms to Remember:** - **Principal (P):** Amount of loan - **Period (N):** Time taken to return the loan - **Interest (I):** Extra money paid at the time of returning the loan - **Rate of Interest (R):** The percentage at which interest is calculated (P.C.P.A. = Percent per annum) - **Amount:** Principal + Interest **Formula for Simple Interest:** $$ \text{Simple Interest} = \frac{P \times N \times R}{100} $$ **Note:** If Period (N) is given in months, then divide by 12 months. ### Compound Interest By applying the formula of C.I.: $$ \text{CI} = P \left( 1 + \frac{R}{100} \right)^N - P $$ ### Discount The following formulae are used to solve problems based on discount: 1. **Discount:** List price - Selling price 2. **Rate of Discount:** $$ \frac{\text{Discount} \times 100}{\text{Point Price}} $$ 3. **List Price:** $$ \frac{\text{Discount} \times 100}{\text{Discount \%}} $$ 4. **Due Price:** Point Price - Discount 5. **Trade Discount:** $$ \frac{\text{Trade Discount \%} \times \text{List Price}}{100} $$
