Add a same natural number to the numerator and denominator of 1 / 13 at the same time to get another fraction equal to 1 / 2. What is the natural number?

Add a same natural number to the numerator and denominator of 1 / 13 at the same time to get another fraction equal to 1 / 2. What is the natural number?

Let the natural number be a, then
(1+a)/(13+a)=1/2
2+2a=13+a
a=11

If the numerator denominator of 1 / 15 is added with the same natural number at the same time, the new fraction obtained is equal to 1 / 3

6

If three consecutive natural numbers are multiples of 17, 19 and 21, then what is the minimum number of the first of the three consecutive natural numbers?
As above

Let the first number be x, x = 17a, x + 1 = 19b, x + 2 = 21C (where: A, B, C are positive integers) a = (21c-2) / 17 = C + 2 (2c-1) / 17, B = (21c-1) / 19 = C + (2c-1) / 19 (2c-1) / 17 and (2c-1) / 19 are integers. The minimum value of 2c-1 is 17 * 19 = 323, and the minimum value of 162 x is 21 * 162-2 = 3400

Three consecutive natural numbers, in turn, are multiples of 15.17.19
RT

2430,2431,2432