Find the sum of all natural values n satisfying the LCM condition (n; 45) = 45.

To calculate the sum of all natural values of n that satisfy the LCM condition (n; 45) = 45, first we find all possible values of n. Since the LCM (n; 45) is equal to the number 45 itself, 45 is a multiple of n. To find all divisors of 45, we factor this number into prime factors:

45 = 3 3 5.

So n can be prime 3 or 5.

now we will find all composite factors of 45, multiplying its prime factors in all ways:

3 * 3 = 9;

3 * 5 = 15.

Hence, n = 1; 3; 5; nine; 15; 45.

We calculate their sum: 1 + 3 + 5 + 9 + 15 + 45 = 969.