Question
Find the largest 5-digit number that is divisible by 12,
15, 18, and 24. Also, what is the remainder when this number is divided by 11?Solution
Step 1: Find the Least Common Multiple (LCM) of 12, 15, 18, and 24. Prime factorization: 12 = 2² × 3 15 = 3 × 5 18 = 2 × 3² 24 = 2³ × 3 LCM = 2³ × 3² × 5 = 360. Step 2: Find the largest 5-digit number divisible by 360. The largest 5-digit number is 99999. Divide 99999 by 360: 99999 ÷ 360 = 277.77 (take the integer part, 277). Multiply 277 by 360: 277 × 360 = 99720. Step 3: Find the remainder when 99720 is divided by 11. 99720 ÷ 11 = 9065, remainder 5. Correct Option: d
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