Find the LCM of the given numbers.

$$
12 = 2^2 \times 3
$$
$$
30 = 2 \times 3 \times 5
$$

$$
\text{LCM}(12, 30) = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = \boxed{\text{60}}
$$

$$
16 = 2^4
$$
$$
50 = 2 \times 5^2
$$

$$
\text{LCM}(16, 50) = 2^4 \times 5^2 = 16 \times 25 = \boxed{\text{400}}
$$

$$
18 = 2 \times 3^2
$$
$$
20 = 2^2 \times 5
$$
$$
36 = 2^2 \times 3^2
$$

$$
\text{LCM}(18, 20, 36) = 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = \boxed{\text{180}}
$$

$$
55 = 5 \times 11
$$
$$
70 = 2 \times 5 \times 7
$$
$$
77 = 7 \times 11
$$

$$
\text{LCM}(55, 70, 77) = 2 \times 5 \times 7 \times 11 = \boxed{\text{770}}
$$

$$
45 = 3^2 \times 5
$$
$$
60 = 2^2 \times 3 \times 5
$$
$$
90 = 2 \times 3^2 \times 5
$$
$$
120 = 2^3 \times 3 \times 5
$$

$$
\text{LCM}(45, 60, 90, 120) = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = \boxed{\text{360}}
$$

$$
24 = 2^3 \times 3
$$
$$
36 = 2^2 \times 3^2
$$
$$
60 = 2^2 \times 3 \times 5
$$
$$
\text{LCM}(24, 36, 60) = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360
$$

$$
N + 11 = 360
$$
$$
N = 360 - 11
$$
$$
N = \boxed{\text{349}}
$$

$$
20 = 2^2 \times 5
$$
$$
50 = 2 \times 5^2
$$
$$
75 = 3 \times 5^2
$$
$$
\text{LCM}(20, 50, 75) = 2^2 \times 3 \times 5^2 = 4 \times 3 \times 25 = 300
$$

$$
N - 7 = 300
$$
$$
N = 300 + 7
$$
$$
N = \boxed{\text{307}}
$$