True or False:
If N > K > p > q, if K is the LCM of p & q, if N divided by p has a remainder of x, and if N divided by q has a remainder of y, then the remainder when N is divided by K is the LCM of x & y.
False. Let q = 3, p = 5, so K = 15, and let N = 37. Then
37 divided by 3 → remainder = 1
37 divided by 5 → remainder = 2
37 divided by 15 → remainder = 7
and 7 is NOT the LCM of 1 & 2. This rule doesn't work at all.