Question : Find the smallest number which when divided by 19 and 23 gives remainders of 13 and 17 respectively.
Option 1: 419
Option 2: 429
Option 3: 431
Option 4: 437
Correct Answer: 431
Solution :
The difference between divisor and remainder,
i) 19 – 13 = 6
ii) 23 – 17 = 6
The difference between the divisor and remainder is the same.
The LCM of 19 and 23 is 437.
To get the smallest number, which gives the remainder of 13 and 17 when divided by 19 and 23, we have to subtract 5 from the LCM of 19 and 23.
The smallest number = LCM – 6 = 437 – 6 = 431
Hence, the correct answer is 431.
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