The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 24 and 64 have in common.

Latoya scored 78% on the test meaning she earned 78% of the possible points on the test. There were 300 possible points on the test so she earned 300 x 0.78 = 234 points. Each question is worth 3 points so she got \( \frac{234}{3} \) = 78 questions right.

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{3}{100} \) x 8 = \( \frac{3 \times 8}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour

So, in an average hour, the machine will produce 8 - 0.24 = 7.76 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 7.76 = 170.7 error free parts were produced yesterday.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{6} \) x \( \frac{4}{6} \) = \( \frac{3 x 4}{6 x 6} \) = \( \frac{12}{36} \) = \(\frac{1}{3}\)