Answer
greatest common divisor = 6
least common multiple = 900
Work Step by Step
Factor each number completely to find:
$36 = 6(6) = 2(3)(2)(3)=2(2)(3)(3)
\\150 = 25(6) = 5(5)(2)(3) = 2(3)(5)(5)$
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 - two times
3 - two times
5 - two times
Thus, the LCM of the two given numbers is:
LCM = $2(2)(3)(3)(5)(5) = 900$
