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Find the GCF and LCM of the numbers:
a) 45, 150
b) 68, 102

User Bic
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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

User Puneet
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