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Question
What is the sum of digits of the least multiple of 13, which when divided by 6, 8, and 12 leaves 5, 7, and 11 as the remainder?
What is the sum of digits of the least multiple of 13, which when divided by 6, 8, and 12 leaves 5, 7, and 11 as the remainder?
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Solution
The correct option is D 8
Least number which when divided by 6, 8, and 12 leaves 5, 7, and 11 as the remainder is LCM [6, 8, 12] - 1 = 23.
So the required number is of the form 23 + 24k
Now the least number which is of the form 23 + 24k and multiple of 13 is 143.
Therefore, sum of digits = 1 + 4 + 3 = 8
Least number which when divided by 6, 8, and 12 leaves 5, 7, and 11 as the remainder is LCM [6, 8, 12] - 1 = 23.
So the required number is of the form 23 + 24k
Now the least number which is of the form 23 + 24k and multiple of 13 is 143.
Therefore, sum of digits = 1 + 4 + 3 = 8
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