Final answer:
The GCF of 45 and 150 is 15, and the LCM is 450. The GCF of 68 and 102 is 34, and the LCM is 204.
Step-by-step explanation:
To find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of the given numbers, we can use the prime factorization method.
a) 45, 150:
Prime factorization of 45 = 3 x 3 x 5
Prime factorization of 150 = 2 x 3 x 5 x 5
GCF = Product of common prime factors = 3 x 5 = 15
LCM = Product of highest powers of all factors = 2 x 3 x 3 x 5 x 5 = 450
b) 68, 102:
Prime factorization of 68 = 2 x 2 x 17
Prime factorization of 102 = 2 x 3 x 17
GCF = Product of common prime factors = 2 x 17 = 34
LCM = Product of highest powers of all factors = 2 x 2 x 3 x 17 = 204