#### Answer

greatest common divisor = 6
lease common multiple = 240

#### Work Step by Step

Factor each number completely to find:
$30 = 6(5) = 2(3)(5)
\\48 = 6(8) = 2(3)(2)(2)(2) = 2(2)(2)(2)(3)$
Greatest Common Divisor (GCD):
Note that the common factors to both numbers are:
2 (once)
3 (once)
Thus, the GCD of the two numbers is:
GCD =$2(3) = 6$
Least Common Multiple (LCM):
Take note of the maximum number of times that each unique factor appears in the factorization of the two given numbers:
2 - four times
3 - once
5 - once
Thus, the LCM of the two given numbers is:
LCM = $2(2)(2)(2)(3)(5) = 240$