Question
Find a number between 100 and 200 that leaves a
remainder of 3 when divided by 8, 12, or 15. Once identified, determine the remainder when this number is divided by 17.Solution
Let the number be n+3.
This means that n is completely divisible by 8, 12, 15 or n is a multiple of LCM of 8, 12 and 15.
=> n is a multiple of 120
Since the number lies between 100 and 200, the number must be 123.
123 = 17x7 + 4
Hence remainder = 4
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