Find the LCM and the GCF of 100 and 120.
A)120, 20
B)600, 40
C)600, 20
D)12,000, 40

Question

Quizplus · Accepted Answer

To find the LCM and GCF of 100 and 120, we can use prime factorization.

100 = 2^2 × 5^2
120 = 2^3 × 3 × 5

To find the LCM, we need to find the product of the highest powers of all prime factors involved:

LCM = 2^3 × 3 × 5^2 = 600

To find the GCF, we need to find the product of the lowest powers of all common prime factors:

GCF = 2^2 × 5 = 20

Choice C is the best choice, as it correctly provides the LCM as 600 and the GCF as 20.