The sum of the digits of n is 12.
Given data;
The greatest common divisor of n and 45 is 15, whereas the least common multiple of n and 18 is 180.
To get the sum of the digits of n;
Let,
LCM (n, 18) = 180
GCD (n, 45) = 15
(I) LCM (n, 18) = 180 = n must be the divisor of 180
Divisors of 180 ⇒ 1, 2, 3, 6, 9, 10, 18, 180
As 1, 2, 3, 6, 9, and 18 are divisors of 18.
The smallest n is 9.
(II) GCD (n, 45) = 15 = n has a factor of 3 and 5
So, n = 3
Therefore, the sum of the digits of n is 12.
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