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
Step 1: Find the prime factorization of each time period. Time for the first hand to go around = 8 seconds 8 = 2 × 2 × 2 = 2^3 Time for the second hand to go around = 6 seconds 6 = 2 × 3 Step 2: Calculate the least common multiple (LCM) of 8 and 6. The LCM is the product of the highest powers of all prime factors present in either number. LCM(8, 6) = 2^3 × 3^1 = 8 × 3 = 24 Step 3: The hands will next be together at the top of the dial after the LCM of their individual rotation times. The hands will next be together at the top of the dial after 24 seconds. The hands will next be together at the top of the dial after 24 seconds. 3 done, 2 left today. You're making progress.