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: Tafuta vipengele vikuu (prime factors) vya kila muda wa kengele. Kengele ya kwanza: 24 = 2 × 2 × 2 × 3 = 2^3 × 3^1 Kengele ya pili: 30 = 2 × 3 × 5 = 2^1 × 3^1 × 5^1 Kengele ya tatu: 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2 Step 2: Tafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha 24, 30, na 36. LCM inapatikana kwa kuchukua kila kipengele kikuu kwa nguvu yake ya juu zaidi inayopatikana katika vipengele vya namba hizo. LCM(24, 30, 36) = 2^3 × 3^2 × 5^1 LCM = 8 × 9 × 5 LCM = 72 × 5 LCM = 360 dakika Hii inamaanisha kengele zote zitapiga tena pamoja baada ya dakika 360. Step 3: Tafuta idadi ya mara kengele ya dakika 24 itapiga ndani ya dakika 360. Ili kupata idadi ya mara kengele ya dakika 24 itapiga kabla hazijapiga zote pamoja tena, gawanya muda wa LCM kwa muda wa kengele hiyo. Idadi ya mara = LCMMuda wa kengele ya 24 Idadi ya mara = 360 dakika24 dakika Idadi ya mara = 15 Kengele ya dakika 24 itapiga mara 15 kabla hazijapiga zote pamoja tena. Idadi ya mara kengele ya dakika 24 itapiga ni 15. That's 2 down. 3 left today — send the next one.