If a number 'a' is divisible by 18 and another number

Solution

Given that a is divisible by 18 and b is divisible by 12, we need to determine what a²-b² is divisible by. The expression a²-b² can be factored as= a²-b²= (a-b) (a+b) Since a is divisible by 18, a can be expressed as a = 18m for some integer m. Since b is divisible by 12, b can be expressed as b = 12n for some integer n. The least common multiple (LCM) of 18 and 12 is 36. Therefore, both a band a+b is divisible by 6 (since they are sums or differences of multiples of 18 and 12). Thus, (a²-b²) is divisible by 36