What is the sum of digits of the least multiple of 13 which when divided by 6 8 and 12 leaves 5 7 an...........

Quantitative Aptitude (CDS) LCM, HCF

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 respectively as the remainders?

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Explanation:

LCM of 6, 8, 12 is 24
Number is when divided by 6, 8 and 12 leaves 5, 6
and 11 as remainders, as 6 – 5 = 1, 8 – 7 = 1, 12 – 11
= 1 So (24 k – 1) will be divisible by 13.
⇒(24k−1)/13
, is divisible fork_min = 6
At k = 6, Number is = 24 k – 1
= 24 × 6 – 1 = 143 => Sum of its digit = 1 + 4 + 3 = 8