Find the lcd for the following pair of fractions. 17/18 and 1/45

The least common denominator (LCD) is the smallest multiple of both 18 and 45. Easiest way is to find the prime factors of both numbers, then collect the prime factors that appear the most number of times in both lists.

18 = 2 x 3 x 3
45 = 3 x 5 x 5

2 appears once in the first list, none in the second. once is the most times.
3 appears twice in the first list, once in the second. twice is the most times.
5 appears twice in the second list, none in the first. twice is the most times.

2 x 3 x 3 x 5 x 5 =  450 is the LCD

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)