What is the largest number k less than 1000 such that the remainder is 1 when k is divided by each of 3, 4, and 5?
+9 961. lcm(3,4,5) = 60 so k will be in the form ----> k = 60n + 1 for some integer n
the problem asks for largest k less than 1000 so: k < 1000 ----> 60n+1 < 1000
solving for n the inequality yields n < 17 and since we are looking for greatest int less than 1000 then n will equal 16 in this case to maximize k.
plugging in n = 16
k = 60(16) + 1 = 961
