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.
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6. Kengele katika shule ya Provident inalia kila baada ya dakika 12 na kengele kutoka shule ya Soaring inalia kila baada ya dakika 18. Ikiwa kengele zote mbili zilia pamoja saa 8:20 asubuhi, baada ya dakika ngapi zitalia pamoja tena? Ili kujua baada ya muda gani kengele zitalia pamoja tena, tunahitaji kupata Kigawo Kidogo Zaidi cha Pamoja (LCM) cha nyakati zao za kulia. Step 1: Tafuta vigawo vikuu vya kila nambari. Kwa dakika 12: 12 = 2 × 6 = 2 × 2 × 3 = 2^2 × 3^1 Kwa dakika 18: 18 = 2 × 9 = 2 × 3 × 3 = 2^1 × 3^2 Step 2: Pata LCM kwa kuchukua nguvu ya juu zaidi ya kila kigawo kikuu kinachoonekana katika vigawo vyote. LCM(12, 18) = 2^(2,1) × 3^(1,2) LCM(12, 18) = 2^2 × 3^2 LCM(12, 18) = 4 × 9 LCM(12, 18) = 36 Hii inamaanisha kengele zitalia pamoja tena baada ya dakika 36. Jibu ni dakika 36. Dakika 36 3 done, 2 left today. You're making progress.