Let N be the least positive integer such that

Question

Let N be the least positive integer such that

Let N be the least positive integer such that whenever a non-zero digit c is written after the last digit of N, the resulting number is divisible by c. Then the sum of the digits of N is:-

(a) 9

(b) 18

(c) 27

(d) 36

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

The correct option is (a) 9.

N is least positive integer and when a digit c is written after last digit of N, the resulting number is divisible by c.

⇒ So, (N)c / c

Least positive integer (N) which is divisible by digit c i.e. (1−9)

So possible number is

⇒ (9 × 8 × 7 × 5)c / c

Number, 9 × 8 × 7 × 5 is divisible by all the digits from 1 to 9

⇒ So, Number is 72 × 35 = 2520 = N

⇒ Sum of the digits of number N = 2 + 5 + 2 + 0 = 9