## Thinking Mathematically (6th Edition)

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 = $2(2)(2)(2)(3)(5) = 240$