This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — here are the solutions to your questions: Question 27: a) Find the L.C.M of 6 and 9. Step 1: Find the prime factorization of each number. 6 = 2 × 3 9 = 3 × 3 = 3^2 Step 2: To find the L.C.M, take the highest power of all prime factors present in either number. L.C.M(6, 9) = 2^1 × 3^2 = 2 × 9 = 18 The L.C.M of 6 and 9 is 18. b) Find the smallest number when divided by either 7 or 8 the remainder is 4. Step 1: Find the L.C.M of 7 and 8. Since 7 and 8 are coprime (they share no common factors other than 1), their L.C.M is their product. L.C.M(7, 8) = 7 × 8 = 56 Step 2: The number we are looking for, when divided by 7 or 8, leaves a remainder of 4. This means the number is 4 more than a multiple of the L.C.M of 7 and 8. Smallest number = L.C.M(7, 8) + 4 = 56 + 4 = 60 The smallest number is 60. What's next? 📸