could you please me help me with these three discrete math question????

. Let a and b be two integers and n be a natural number. Show that n divides a b if and only a and b have the same remainder when divided by n. . Given two natural numbers a and b, let lcm(a, b) denote the smallest natural number that is divisible by both a and b. For example, lcm(4, 6) = 12. Show that lcm(a, b) = #211,). . Let p be a prime and a1, . . . , an be natural numbers, Where n 2 1. Show that if p divides a1 . . . an, then p divides at least one of the numbers (11, . . . , an