1. The HCF of two numbers is 12 and their LCM is 180. If one number is 36, find the other number.
We use the fundamental relationship between HCF, LCM and two numbers which states that product of two numbers equals product of their HCF and LCM. Given: HCF equals 12, LCM equals 180, First number equals 36. Formula: First number times Second number equals HCF times LCM. Therefore: 36 times Second number equals 12 times 180 equals 2160. Second number equals 2160 divided by 36 equals 60. Verification: HCF of 36 and 60 equals 12. LCM of 36 and 60 equals 180. Both conditions satisfied.
// Formula: Number1 × Number2 = HCF × LCM // Given: // HCF = 12 // LCM = 180 // Number1 = 36 // Number2 = ? // Calculation: // 36 × Number2 = 12 × 180 // 36 × Number2 = 2160 // Number2 = 2160 / 36 // Number2 = 60 // Verification: // HCF(36, 60) = 12 ✓ // LCM(36, 60) = 180 ✓