What is the highest number between 5000 and 5500, which when divided by 12,16 and 24, would leave a remainder 9?
Given:
Range: 5000 to 5500
Divisors: 12, 16, 24
Remainder: 9
Formula Used:
LCM of divisors to find the common multiple.
LCM × n + remainder to calculate the number.
Solution:
LCM(12, 16, 24) = 48
Possible numbers: 5000 ≤ (48 × n + 9) ≤ 5500
For n = 104: 48 × 104 + 9 = 5016 + 9 = 5025
For n = 114: 48 × 114 + 9 = 5472 + 9 = 5481
For n = 115: 48 × 115 + 9 = 5520 + 9 = 5529 (Exceeds 5500)
5481 is the correct answer.
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What is the highest number between 5000 and 5500, which when divided by 12,16 and 24, would leave a remainder 9?
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